"It's wearing me thin" means it's making me less patient. I am losing my patience.

Hello Yljaha, I haven't heard this expression before and there doesn't seem to be much about it on the internet, I suspect it may be a version of wearing me out/down. Ie making me tired/weaker. Hope this helps Bob

Thank you, Peachey, now I understand the origin of that expression)

I agree with Abby - we do say "my patience is wearing thin". "Wear" here means something rubs and erodes your patience, until your patience is worn out.