Generally, as long as you're not going too extreme there isn't an issue with wearing a plug for an extended period of time. Many people will find that it gets uncomfortable as the lube dries out or otherwise migrates away from the plug and anus, but you won't damage yourself.

Occasionally a large, hard base might chafe (minor), or it may be possible in theory for a very large plug to be large enough to cause problems with diminished circulation or other pressure issues, but for the most part you won't have any problems even wearing it for 24 hours plus.