In my exoperience, sphagnum peat moss (s.p.m.) when dry does not absorb water readily. If you are using pure s.p.m. that would explain the water flowing right through. You are using a coconut fibre basket which would dry out your s.pm. very quickly as well because air can just flow right through. If the s.p.m. is kept continueously wet then there is no problem. It would absorb alot of water everytime you water. But using just s.p.m. for Neps media is not so good as there is little air for the roots.
I would suggest mixing your s.p.m. with sphagnum moss. It is also best to have some coarse material in the media like coconut chips, polysterine pieces, coarse perlite, etc.
Just what I think from my experiece.