What site is this? Have you tried asking their staff about it?
It is PrimeDice. I don't know what is maximum bet amount there because I am not a high roller. But based on this error it is 0.04 BTC.
However, this is their official thread you should ask there:
https://bitcointalk.org/index.php?topic=208986.0It is highly active you will get your answer in no time. My initial guess is that any bet exact/lower than 0.039 BTC would be fine. But I will ask about this to be sure.