For those who recently acquired privileges through reputation, it would be nice to be notified when starting a bounty which privilege will be revoked if any.
As Pesto and TheTXI pointed out, the underlying problem is that people don't understand that if they fall below one of the reputation thresholds in the FAQ, they lose the privileges that come with that threshold. This should probably be stated clearly in the FAQ, just to raise general awareness.
I still think a warning when posting a bounty would go a long way toward raising awareness of the issue. It would definitely be helpful to put the information right in front of people who are about to willingly take a loss in rep by posting a bounty. There are very few ways to lose significant amounts of reputation on Stack Overflow. Posting a bounty is the most common, and the only way that is 100% voluntary (massive downvoting, flagged as offensive, and reputation recalculation are the others). Explicitly telling people they are about to lose a hard-won privilege along with the reputation points seems reasonable to me.
I don't think the key problem is a lack of notification that bounties cost rep. The problem is that people are still under the impression that reaching the rep required for an ability means that they will always have that ability. It's a fundamental misunderstanding of how rep works, which needs better education than a warning when setting a bounty.
I think it would be better just to have a note or something saying "If rep lost via a posted bounty drops down below a certain privilege level, you will lose privileges until rep is regained".
Or just make the user use basic subtraction and figure it out on their own and make it better known throughout the site that your rep can go up and down, and so can your privileges based on that rep.
The new privileges page and notifications do a lot to raise awareness.
New users are now notified quite aggressively when they gain new privileges. We also show them clearly what reputation score is required for each privilege.
I'd suggest that the user be able to keep the functionality/privilege unless the hitpoint were gained in frowned-upon ways. From what I understand, hitpoints are indicators of "how much the site trusts" a user. If a user has reached a threshold, and then decides to give it all away in bounty, I'd argue that the person is still entitled to be trusted.
I understand though that the implementation is probably set up to check the current hit points, not a flag that indicates if they ever reached some threshold.
from here :
Remember, Stack Overflow is run by you! If you want to help us run the site, you'll need reputation first. Reputation is a (very) rough measurement of how much the Stack Overflow community trusts you. Reputation is never given, it is earned by convincing other Stack Overflow users that you know what you're talking about.
The current implementation makes it clear that this is NOT the case that - that even if you earn the privilege they are transient. As if a person's trustworthiness was transient. I don't see how giving away points via bounty makes a person less "trustworthy" to the "community".
In real life, I would give people privileges once they earned them. I would only revoke them once they did something negative. In this scenario that means that giving bounty, voting down answers or getting down voted is equivalent to doing something negative. That is not how I interpret SO. It is very inconsistent.
Again, I realize that the status quo is to make the code simple to maintain - all one has to do is check the current hitpoint level. That's the only real defense of the policy.