Blocks keep reappearing in a certain area only

This sounds like a spawn protection problem. If all server members are trusted individuals, OP everyone and no one will have any problems. In some cases, deoping everyone can also remove the issue. If you are using plugins or mods, check the config files for that particular plugin or mod. Finally, I'm pretty sure the server owner is able to turn spawn protection off in the vanilla server config file.

Edit:
This question's top answer contains a description of how to enable spawn protection in a large portion of the world by setting the spawn-protection variable in the server.properties file to 999999. I assume that setting spawn-protection=0 in server.properties would disable the effect entirely, and solve your problem.