I haven't found anywhere on Ebay rules that restricts revealing the reserve.
But I do think that many people who ask are trying to find out if you have a reserve that is too low, and then will try to buy the item outside of Ebay.
But you do have to remember that in the case of having a reserve, it is an auction. And if you go to a real live auction, for instance a classic car auction, their will be many cars with a reserve. That's to protect the seller. Its an accepted auction practice. The auctioneer doesn't call out "And the reserve is $50,000" LOL. If you shouted out "What's the reserve" probably two dour faced strongarms would kindly escort you off the premises.
There are no guarantees at a real live auction, other than if you got the bucks and are the high bidder and meet the reserve, its yours. If there's an item you really want and have been looking for awhile for it, bid high. Is it fair? Not really. That' how it is in the big world. And just about everything at an actual auction is sold as is, except maybe works of art . Didn't see that crack on the bottom of the priceless vase before you bid, too bad.
I typically use reserves on the more expensive items. Its to prevent giving it away. Sometimes if there is little action on an item, lowering the reserve is a good idea, probably cheaper in the long run than having to relist it. So sometimes I set the reserve a little high, knowing that it can be lowered.
I know a guy who starts all his auctions at a fairly high price, and notice that he has to relist many of them. A lower starting price really does seem to help, but only if someone bids fairly early and gets it going. Seems like in the last year or so more Ebay buyers have been holding off and bidding at the last moment.
And like several folks have mentioned, on some items which didn't sell I have relisted them at higher prices and they have sold - its all a perception thing about worth.
During these slow days of summer, using a BIN seems to work better. People just aren't logged in as much during these vacation months and don't want to wait around and remember to bid on an item when it ends. They seem to lose patience, they want the item but are distracted.