One of the lines goes:
"The maximum number of soulmelds that you can have shaped simultaneously is equal to your Constitution score minus 10 or the number of soulmelds allowed for your level, whichever is lower."
Thus, if your Con became 10 for whatever reason, you couldn't have any soulmelds shaped. Which would likely mean if you had some shaped when you got Con damaged, they'd become either unshaped or suppressed and useless. If they became suppressed, bringing one's Con back up to supporting levels would seem to let them function as normal. If they become unshaped, then they can't be shaped again until after the victim rests and does the usual stuff for being able to shape them again.
Based on how the spell Unshape Soulmeld is 4th level, unshaping melds is at least recognized as a moderately powerful effect. The intent could go either way. Likewise, the reasonability of it could go either way since ability damage is meant to be a big deal and thus will screw over characters for the duration of the effect. However, depending on the tone of the game, such a screw over might not be appropriate.
Yes, it's probably down to how the DM does things. It's a pity WotC couldn't put in the actual interactions for this kind of thing because it's a rather annoying effect.
I'd probably go for a middle ground on it and say that ability damage will initially suppress the soulmelds, but after a certain amount of time if the ability damage is still there then the melds are unshaped and the character needs to get the damage healed and go through the process of shaping melds again to benefit from them. I'd probably do the same thing for spells and psionics too. What that time limit might be, I'm not entirely sure on yet since it'd have to be short enough where the character could actually have the ability restored (which means at least 3 rounds due to the Restoration line's batshit crazy casting time). I'd say anywhere between 10 minutes to an hour would do..