Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do what I can to provide the right answer to your question.
First, I advise that you make sure the a-few-hours-then-stops status, is (or, is not) present even when you are not using your router at all.
To test that, simply use only one computer, directly connected to your Linetec LT150MR. For about 6 hours, to be quite sure.
Second, is your router a D-Link brand router? (or any brand but Netgear or Linksys or Cisco-Linksys...) if so, it is quite probable that the failure is essentially the router, not anything to do with configuration. Off-brand router names do often fail in something like the fashion you describe: being unable actually maintain a connection. And, even the good brand names occasionally fail.
Third... Given the above, I don't think that the difference between static and dynamic IP is significant.