This is absurd. There is no chance your applications will close by themselves. On a windows VPS you would connect via Remote Desktop, run your applications, and then disconnect. Everything you left running will be there 100% (make sure you turn off auto-updates or it might reboot)
There are lots of good VPS solutions out there, you need to find the provider that best suits you. What country do you want it hosted in? What type of specs do you need? What is your budget.
Whenever I need to find a new host I head over to webhostingtalk.com and start searching. Here is a link to their VPS special offers forum, I am sure you can find something : http://www.webhostingtalk.com/forumdisplay.php?f=104