There is a one program that does something suspicious when it's been on for a very long time. I would like to speed up Virtualbox guest so that I get closer to the moment when suspicious behavior starts. Can I for example make it run at 4x speed?
Unfortunately, no. VirtualBox and other virtualization platforms provide virtual hardware, and AFAIK not a single one of them is able to speed things up like that.
Instead you should graph your virtual server with Cacti or similar, monitor the processes the server runs and that way get a clue what's going wrong with the server.