@RezonantVoid that's a tricky one, I used to have so much drama with it and always used to look awful after a week.
Not sure what type it is we have it on all of our bonsai's as well but is common here, I tend to go for the flat growing types of moss, any of those thick, cushiony types need more airflow through them and more uv.
The pH of peat is very acidic around 4 from memory which doesn't help, moss will flourish at 5.5 which is acidic but mainly because nothing much else grows there.
So, opening the lid to allow for gas exchange, making sure there is enough ambient light, moisture etc are all things to try.
Moisture is a fine line, as too wet will grow mildew which will kill it and too dry doesn't help.
When installing it, really push it in firm and make sure that your substrate is packed well, give it a good first soak and push it in again.
Chlorinated water from the tap will give moss a hard time too, all we have here on my farm is rainwater.
Here is a link to the layout of the enclosure- http://arachnoboards.com/threads/enclosure-terrarium-pictures.48951/page-84#post-2912702 I made this tank a week or so before these were taken and let it rest first.
Next time I post some critters to you I will put a sheet of this moss in if you like