My current mouse is a several year old Darkfield-type from Logitech, and my current computer is an HP Pavilion x360 laptop running Windows 10.
About a week or 2 ago, I started having issues where the cursor would stop registering movement for about half a second at a time. This seems to happen on a variety of different surfaces, so I don't think that's the problem.
Is the mouse just getting old, or is there something I can do to fix it?
Not an unknown issue. Clean the optical sensor/laser port area under the mouse. Disassembly is not required. Use a clean Q-Tip, lightly moistened with water. Should that not resolve the issue, and if Tetsujin's suggestion above is also fruitless, contact Logitech Support.