Also, I have another possibility for the problem: During my reshuffling of my space fleets, I accidentally gave a large space construction scow to the other race. It's got no sensors except the tiny close-range thermal sensors, but is sitting right on top of the highest traffic area in known space. Is this maybe part of the problem. Is there a way to delete this ship without hitting it with an alpha strike? I don't want to piss off the gliesens...they're cute and very nice.
I do believe we have a winner! Small sensors in a busy area, populated primarily by a different empire's shipping, will require frequent checks for sensor contacts. I do not know how to delete an NPR's vessels. However, if the ship in question can not be removed from play, you may be able to minimize the impact it's sensors have on sensor checks. Build a PDC with maximum size and sensitivity thermal sensors on the planet the S.S. Myopic is orbiting, and give it to the locals. Sensor checks will still occur, but should progress much more quickly than before, as things are simply considered to be in range, and are not running into and out of sensor range at 5 second intervals.
Be careful though, when designing your thermal sensor. Make sure that the range it covers for small strength signals does not exceed the integer buffer. Or, simply design a thermal sensor which can detect a strength 5 thermal signature at a range slightly larger than the radius of the entire system, and can always cover the jump points.
Finding a way to simply delete the ship from space and time may be a better option, though.