After having searched for previous forum posts it appears to me that this problem isn't perhaps so easy to fix as it maybe seems (also given the apparent different ways that Systems/OSses seem to handle this).
E.g. in a fairly recent post ("monitor standby") also the opposite is stated from what you've been reporting since quite some time already.
Anyhow I include some links to previous threads and can only keep my fingers crossed that BS.Player-team will be able to tackle and solve this matter, which must be quite annoying for BS.Player-users which actively use this energy saving possibility.
When a Bsplayer crash messes up monitor DPMS (power-down) [FIXED] Bsplayer and monitor turn off "Turn off monitor when finished" Monitor doesn't turn off (DPMS) after watching a movie. screen doesn't turning off after using bsplayer odd problems some problems Monitor standby 
[Thanks for your welcome contributions!]