It’s more likely there’s been some other change, e.g. by your ISP.
Did you already have a look at the related troubleshooting support article?
https://support.plex.tv/articles/200931138-troubleshooting-remote-access/
There’s also a guide with some more details
Your server needs to be running somewhere. However there’s options if you don’t want to depend on your desktop to stay up & running all the time, e.g. using a NAS. That being said you should keep in mind that those tend to be significantly less powerful and might therefore not be able to transcode a video if needed.
