I too have been experiencing the "connection problems" for Mega downloads over the last few days. Hadn't changed anything on my end, figured it was something on theirs. After reading over this thread, I checked the box for "use SSL?" in the JD2 plugin settings for Mega.co.nz, and now it appears to be working perfectly fine.
Hopefully word of this gets out – I was able to find it mentioned in a few other places online.