$10 is a bargain. The minimum fee in the various leagues I call is $20, although, come to think of it, I think I recall our MSBL league is going to experiment this year and do away with the protest fee.
I think a protest fee should be high enough to dissuade the manager from protesting frivolously, but low enough to not pose an undue burden when a legitimate issue of controversy exists. In other words, twenty bucks.