How To Troubleshoot A Linux VPS With CPanel

I'm having some problems with my new VPS server. The server is running under Linux with Plesk (sorry type error on the title, it's not CPanel but Plesk instead).

The server is working fine most of the time, however, once every one or two weeks, the server can be extremely slow or completely down. The only thing that I can do the solve the problem is to restart the server. Once the server is restarted, everything is back to normal. There's once, I couldn't even go to the control panel, the server restarted by itself after 45 minutes later.

I tried contacted the server administrator, they said they couldn't do any debugging for me since I have restarted the server. Their response is very slow, I couldn't wait for a few hours just to let them troubleshoot. And since this is unmanaged VPS, they seems to be reluctant to teach me on how to troubleshoot it. They just asked me whether I had done some troubleshooting whether it's a DDOS attack or just some optimization is required for the server. They are asking back the question to me! Due to some reasons, we can afford a downtime of more than half a day to switch the server, so meantime, I have to learn on troubleshooting the problem myself.

So, I will like to know if similar things happened, what should I do? Can I use Plesk to check? Or I need to login using SSH to check the server?