I sometimes have that problem, I solved it by chewing gum. I always chew 2 pieces of Trident Bubblegum on a bike ride. When the gum starts to get too hard, I swallow it (yes, I am serious) and I chew a new piece. I keep a pack of gum in my bag.
I am guessing that the gum keeps the mouth loaded with plenty of saliva which keeps the old whistle wet. I hate when I forget it, because I use up water faster. I have asthma so it is important to keep the mouth and throat nice and moist. Hope this helps.
By the way for those of you who can't believe I swallow my gum, I also swallow cherry pits and watermelon seeds. I would much rather swallow them, then be rude and spit them out. Who doesn't hate stepping in gum!!!!!???? Believe me, they do not get stuck in your appendix, they come out just like everything else!