Learn English – It’s certainly not a given

In addition to using Mark Hubbard’s “Thank you in advance for [keeping me informed]” (or just “Thanks in advance for [ … ]” in less formal situations) to express your thanks in advance without having to rely on context, you could also consider using a near-synonym for being thankful to use with the conditional would, for example:

“I would (I’d)[ greatly/very much] appreciate your keeping me informed.”

or (to emphasize the conditional notion even further):

“I’d be [extremely/very] grateful if you would (you’d)/could keep me informed.”

(Please note that, although it’s probably overstating the actual level of appreciation/gratitude, I think I would include greatly and extremely, especially in the above, “in advance” cases, but probably less so in the “after the fact” cases mentioned below. However, be careful not to “over-do” it because you could come across as being sarcastic or “sycophantic” [the English sense!], so on second thought, maybe the more restrained very/very much would be better in these cases where intensifying the gratitude might be in order because you are actually requesting a future favor at the same time.)

Regarding “after the fact” expressions of thankfulness (such as the one you made on “Overflow” and are asking about here), in addition to Mark’s use of the past tense (provided) or relying solely on context (which I agree can be ambiguous, especially in your example where it could easily be interpreted as an on-going request), you could consider changing “keeping” to “having kept” and “keep” to “kept” to use either with the same near-synonyms above (but in the unconditional present) or else (preferably, I think) simply with the original “Thank you/Thanks” construction, for example:

“I [do] [greatly/very much] appreciate your having kept me informed.”
(where the do would be an optional way to emphasize the appreciation)

“I am (I’m) [extremely/very] grateful that you kept me informed.”

Thank you (Thanks) for having kept me informed.

(But please see this relevant Word Reference thread that seems to confirm that we are, in fact, often (but not always?) at the mercy of sometimes ambiguous context in English (as indicated in user3169's answer). At least “Kelly B” begins his/her answer with “Yes, that's right,” so making the effort in our own speech to avoid the ambiguity would be not only admirable, but also grammatically and logically correct, although we'd still have to rely on context to interpret the meaning when spoken to us by somebody who is less concerned with clarity.)

It means being extremely eager to do something, especially when the haste to do it right away causes problems or errors.

When the Admiral sneezed, junior officers were falling all over each other to pass her a tissue. Two even collided with each other and had to go to sick bay.

Imagine a group of navy officers all pushing one another out of the way to get in the Admiral's good graces.

When Boeing announced their intent to open a new plant, State Governments were falling over each other to offer tax incentives and favourable legal environments.

State representatives, in their eagerness to get a big contract for their state, might find themselves offering so many incentives to the company that they end up losing money overall.

When Michelle, my high-school crush, asked for help with her homework, I was falling over myself to do it for her.

So eager to help the girl that the speaker perhaps put themselves in a bad position.