This is done to prevent (potential) abuse. Unfortunately, you're not given the benefit of the doubt in this case and forced to increase your offer. Here's the explanation on MSE:
As noted by Robert, this has come up recently. Posting a bounty is a
perfectly reasonably thing, a good thing (with badges too!).
However, when applied repeatedly to a question it does start to
To help minimise this, but while leaving open the option of offering a
subsequent bounty when you really, really are looking for another
option we will be implementing a change here, where subsequent
bounties have a higher minimum offering. This means you can't place 6
"cheap" bounties of 50 rep, to keep your answer on the bounty board to
get lots of pass-by upvotes, as subsequent bounties
probably1 will not cover your "spend".
We now double the minimum "spend" for successive bounties on the same
question by the same user. So if you started at 50: your next bounty
on that question has a minimum of 100, the next 200, the next 400, the
Another related change has been mentioned by Sam
- If you are placing a bounty on a question you answered, your minimum spend is 100
1=Unless of course your answer is super-awesome, but if it is
super-awesome it'll probably already be doing the rounds for free
(insert obvious regex/html jape here).