Yep, I've also had the same issue. Its one of the reasons why I always bid early in a round once I've identified a player I am willing to use tokens on. The amount of times I lost players waiting until the last second to bid - and I'm sure I've won players by others doing the same to me - only to see my bid not accepted is stupid.
If you know you want the player it doesn't matter if you bid 1 second into the round as you will only win the round if you are the only bidder.