Fallout Wikia has some tips on recovering lost companions who do not appear in either their original location or the Lucky 38. I have not had this problem myself so cannot test.
Update: I can confirm the Vault 22 method worked for me; successfully recovered Rex (on PC).
For Consoles and PC
Here the given trick is to go to Vault 22 and use the central elevator (requires repair skill level 50).
Choose to go to Level 5 - Pest Control.
The missing Companion(s) may be waiting there at the exit of the elevator, you may need to talk to them and ask them to follow you (ie, they may be stuck in wait mode).
For PC
This involves using the console commands, I highly recommend saving before messing with the console, and as per Xantec's comment you should be aware this will disable Steam achievements for that play session (ie, you need to fix the game then save and restart).
Here <red_id> is an internal number for the companion - for Veronica this seems to be 000e32a9 - you can get the ID's of others from the Wikia site as well.
This will move the companion to your location:
prid <ref_id>
moveto player
This will move you to the companions current location:
player.moveto <ref_id>
If these don't work the recommendation is to kill and resurrent the companion. First use these two:
prid <ref_id>
OpenTeammateContainer 1
This should give you their inventory windows - empty it into your own.
Then do the following, and hopefully the companion should be back:
moveto player
resurrect 1
disable
enable
According to the Fallout Wikia page on Veronica Santangelo she will leave you permanently when destroying the Brotherhood unless you have "high enough reputation", but it isn't more specific than that (see bottom point):
To complete the Mr. House and Caesar's Legion main quest lines it will be necessary to destroy the Brotherhood of Steel bunker in Hidden Valley, which will usually (but not always) cause Veronica to leave the player permanently, even if she is waiting somewhere else at the time. Any items the player gives to her that she has when she leaves the player will stay in her inventory, and it may not be possible to get them back.
It may be possible to get back the gear in her inventory by re-recruiting her (if that option is present), then immediately accessing her inventory via the companion wheel before she has a chance to speak to the player and leave again. You can get the inventory back by pickpocketing her, or killing her when she is walking away.
If the player destroys the Brotherhood bunker prior to meeting Veronica, then tries to recruit her, she will join the player, but almost immediately leave, saying that the player appears determined to fight the Brotherhood.
If the player has a high enough reputation with the Brotherhood of Steel before destroying the bunker, Veronica will not leave.
Best Answer
Hmm, it seems like a stretch but try this:
Travel to Gibsons shack (the one from her quest) and use the terminal on the floor.Click on download research notes and she should magically reappear talking about what technology to go after. Just choose whichever one to make her a follower once again