Is it definitely melamine coated? You can get some chipboard that has a wood veneer instead of melamine.
Also, could the viv be made out of board that has come from furniture? Some of the flat-pack furniture you get has an almost paper-like coating to it - nothing like melamine.
I've used melamine coated chipboard (under the brand name "Contiboard") for viv building for 7 years+ and not had even the slightest bit of water damage to the coating, including vivs that have been sprayed regularly to keep humidity 80%+.
Must admit though I've never kept it continuously wet as it might be with a misting system.
If yours is affected by water it'd be fine to varnish it but give it a good going over with some fine sandpaper to provide a key for the varnish - it'll help to stop it flaking. You may still get some flaking in areas where the board gets hot (near lamps,etc) - you could shield these areas with something, sections of perspex attached with silicone maybe.
Another option could be to coat the surfaces with fablon - self-adhesive vinyl sheet basically. But it can be difficult to get a good even finish, so a few coats with a decent varnish would look better I reckon. Remember to run the viv with the heat on for a while (couple of days at least) before adding the occupant to make sure theres no fumes.
Mark.