The problem is still ongoing, but should be fixed within the next few days. My host has released the following message regarding the problems:
"Recoding has run out of space, literately, so we hope to purchase some more sometime tomorrow, and do a clear up today, sorry for this, if have problems please email support."
There is more to the message, but I reckon that's really all you need to know.

Just a simple problem that shouldn't be overly difficult to fix.