It appears they are partnered with Ubuntu, so I can only guess that it is a custom version of Ubuntu. I'm not saying they keep track of every company, nor do they have to. Minecraft is coded in Java, which is multi-platform. I would assume that there would be no major issues that would occur just because of the Operating System.
The server worked fine for 2 weeks, with the same Operating System. Also, all servers I've visited using the same host have not had this problem. Throwing the problem at an OS issue will not solve the problem any faster.