Is it likely that a factory reset will fix this problem with my laptop?

Look how quick you are

Check router settings. Maybe your neighbors are taking over it.

Mine is doing the same and a reset didn't help. I realize know that the problem is a loose connection. moving or bumping the laptop can cause it to loose connection. opening and closing the screen will sometimes cause it to reconnect. It will usually reconnect on a restart.

sounds like your network driver needs updating that's all . If you can't do that by yourself fined someone who will. Then at that point if it doesn't work you need a new network adapter .

why not just uninstall it and reinstall it?

A good disk cleaning and defrag should help. Install the free version of Wise Care 365 for that. Running the check disk repair utility should help also.

Don't do a factory reset or you will lose programs and drivers plus folders and files. There is a simple and cheap fix assuming your router is working OK. Buy a USB wireless adaptor. Look online for a plug and play one. They are cheap as chips and very reliable. I expect your built in wifi is faulty and the new device will solve your problem.

You can try updating the drivers before doing a factory reset. If that doesn't work, it is probably a hardware problem so factory reset likely will not help. But you can try. Be sure to back up all your files first. And you might have to re-install apps.