Primary Consideration

Due to the controversial nature that this specific problem represents, it takes a mature player and a mature DM to handle this specific scenario well. Ensure that the player and DM have a conversation about something of the magnitude of power revocation BEFORE it is implemented in play...

If you are the DM and this is established as part of your world, ensure that players know this up front if they are considering playing a warlock (or any other class likely to have powers revoked for any reason).

If you are a player and you want this to either be highly probable, talk with your DM. It can create an intriguing story.

Already covered

RAW, there isn't any explicit text that covers a warlock's powers being stripped. Also, there is no class that has rules text covering a loss of powers, save the Paladin whose powers change form when he becomes an Oathbreaker. (DMG p. 97)

Lore from stories associated with various pact-style magic demonstrates and sets precedent that it could be a good story hook, allowing for a very interesting story line that leads to all the things that were mentioned in the original question.

Also Consider

The power belongs to the entity to dole out. If they granted it, it is likely true that they could take it away. This is more of a reference to old literature, to what makes sense, and to what would be fun with the game you and your DM seem to be trying to build.

The rules do not state the specific pact, this is the part that cannot be stressed enough. The power that they currently have should mostly be considered as payment for services rendered. If they are not completely paid for (ongoing payment, for example), then try to avoid stripping a lot of their power from them. Make it minimal, but noticeable. Lower spell slot levels by one levels as that part hasn't been paid in full, if that helps the story line, but do not completely cripple the character.

As for the specific scenario posted in the question:

The devil is highly unlikely to strip power from someone if it is part of a contract. To do so is highly unorthodox for a devil, and would be looked at even more poorly than an upstart servant that the devil couldn't control. The devils live by their contracts, and although adding loop-holes may be favored, rescinding an agreement is not. If a devil were to rescind the power of one of their warlocks, it is likely that another entity would try to mock them by taking the contract instead. This is even more true of a relatively powerful warlock. That said, a devil is also very likely to add a hidden clause that prevents the warlock from using their powers against the devil, with revocation of powers being either temporary or permanent, depending on the devil, the warlock, and the devil's disposition at the time.

They will follow the letter of the contract completely, but don't care about the spirit of the contract. If the devil is powerful enough to grant powers as a patron, they are likely intelligent enough to be more careful about the contract, though a particularly savvy and/or intelligent character could manipulate them in to a contract that is written to the benefit of the character more than the patron (protecting themselves from abandoning the patron, for example).

If you really want to do it

The best way to add the possibility of power revocation for story-line purposes is to ensure that it is an active part of the party's story (as opposed to a passive one). Allow the party to try to stop the powers from getting revoked, or have another patron (possibly a more sinister one) inform the warlock that they are going to lose their powers and offer to be a surrogate patron.

Do something that directly involves the warlock in whether they lose or retain their powers.

In short

Is it possible? Rules don't state that it is, but this is something a DM could easily say yes to with good justification to back it up based on game world.

Should the DM take this path? Probably not, or at least not seriously. If he does, then he should offer a work-around. Don't strip power from a character/player without offering a way of obtaining it again. Don't make the game less fun.

My question: Is this possible?

Yes, it's possible, whether or not the fiend and the god/goddess get along. There is no RAW prohibition from the multiclass, no matter how awkward it looks.

From a purely RAW standpoint, I don't think that Warlocks can lose their powers, but would his good deity even bother with someone who sold their soul to a devil?

This depends on how the DM plays out the deity's and the fiend's role. Points to raise as you two flesh this out (a collaborative effort between you and the DM):

1. How much of a role does redemption play, a deity accepting a lost/troubled soul (bound to a devil) into the fold? The Sword Coast Adevnturer's guide supplement for D&D 5e has some material on FR deities; Baervan gets one sentence of treatment (p. 115) and Chauntea gets a few paragraphs( p. 27). For more detail, you could back up this guidance for Chauntea or Baervan with previously published material and make your case to the DM for why, or why not, either deity fits. Deities thrive on having followers.

2. Playing an internally conflicted character is rich with role playing possibility. Trying to serve the good, still dealing with evil ... that's a standard story IRL, and an element of stories from many different cultures. This would allow the link with the Pit Fiend to remain -- but there's always a price to be paid! (This could provide DM some fun, occasionally at your expense! :) )

   And would that pit fiend continue fueling their powers?

3. Why not? Here's a point of view that the Pit Fiend could take:

   "I've got my hooks into this gnome, I won't let him go. So he wants to get in with that goddess/god? Good! I can use him to cause trouble for (chosen deity), and then enjoy his suffering as he realizes that it's his fault -- due to his hunger for the power only I can give him. Muahahahahaahaa!"

   or

   "I don't like (deity), but we both have (unrelated) unfinished business with that #@!^%$ Orcus, and this gnome will serve nicely as a proxy. In the end, I profit! Muahahahaahaa!"

   You and the DM should be able to work out a deal, and some tension, that fits the campaign.

4. One last point to address as you work with your DM on this multiclass:

   How important is alignment in this campaign?

   Alignment in 5e is a bit different than in previous editions. It is more like an ideal for the character, and a matter of how the player should behave. How well the player character lives up to it, and what the rewards/penalties are, lay in the realm of DM's discretion.

With that in mind, and the two deities to choose from: Chauntea's clerics appear to require a serious commitment, and a decision on being a Pastoral or a True Shaper (the latter looks like a better fit for an adventurer), while Baervan's yoke looks like it is lighter to bear for an adventuring cleric.

Could the pit fiend and the god/goddess get along?

That would require a serious threat that both of them want to counter, something opposed to them both for different reasons ... so that you would be serving both of their interests (roughly) at the same time. Some existential threat to the world itself ... that too lies in the realm of how your DM is running and shaping the campaign.