What in the world could be causing this bathroom sink clog?

This is a regular residential bathroom sink. Granted, it's over a 100 year old house with 100 year old plumbing, but still... so nothing goes into this sink except for toothpaste from regular brushing of teeth, that's it. I pour in some liquid plumr, let it sit overnight, and then the water flows fine. For a while. Give it a day or two, and it gets super clogged again. Is the toothpaste causing the clog? I'm a real loss here because I can't think of what is the cause, and how to permanently fix it...

If you keep pouring liquid plumber down 100 year old drains you will soon be replacing them. The line needs to be snaked.

Never, ever, ever use chemical drain cleaners! Stop it! As johnjh2o states, snake the line. You have one of the most common clogs there is.

I pour _boiling_ hot water down my bathroom drains. It disolves the soap/toothpaste residue without eating away the pipes.

Water is precious but toothpaste will gel up and coat the drain line. Run plenty of water when you are done brushing the pearly whites.

Lavatory sinks are 2nd worst drains to clean behind #1 Urinal drains because of the stinky goo that is coating the drain. Kitchen drains get sludge build up but do not stink nearly as bad as lav sink drains.

even though it is not "politically Correct" to run the water

NOT running the water will cause you to have blockages, .

so be as tree huggy as you want to your friends, but run the water to flush your pipes