You should have the Realtek HD Audio Manager installed, usually has an icon that looks like an orange speaker next to the taskbar clock.

You want to prod settings on there, ideally you want to tell it to tie up all similar jacks (advanced options) and turn off jack insertion detection (there's an icon that looks like a folder above the images of the jacks). The latter's a pretty broke setting, so turning it off normally cures 99% of Realtek issues.

Also dust, make sure the port isn't full of it.