Johny is right, one test you can do is to open up an hyperterminal on Windows and map it to the port of the NMEA0183 string coming from the GPS. After adjusting the speed and format you should see the sentences coming in.
Then leave the laptop for a while until it sleeps, and resume it. If hyperterminal shows the sentences entering again, then you have an issue with MaxSea. But if hyperterminal has lost its connection to the COM port then the issue is within your USB-Serial driver.
The problem with those USB-Serial is that the driver may not support suspend-resume. Maybe you are using the Prolific 2303 that usually come with the Globalsat, in that case i would invite you to test using hyperterminal (or any terminal capable of reading a COM port output in windows) and if it doesn't support suspend-resume then either check the firmware or change for another just to see. The problem can also be in windows...
Here is an excerpt from the documentation of the Prolific 2303:
Finally, the PL-2303 USB to Serial adapter is a fully USB Specification compliant device and therefore supports advanced power management such as suspend and resume operations as well as remote wakeup. The PL-2303 USB Serial cable adapter is designed to work on all Windows operating systems.