I think this happens if you have something in your hands.

you have to empty your hands, as warcryr wrote. Some Patch ago you were able to wring out your clothes even when armed, but this bug has been fixed, so actually it should work when you have empty hands. Works for me anytime with empty hands.

I just had a stroll in the rain on a 3rd p 0.55 server. I tried to wring my clothes, while being careful to have my hands free. I could wring my jeans out with no problem, but my t-shirt was completely intermittent. Sometimes I could wring it out, while other times I couldn't.

Hello BleedoutBill and thank you for the report.
This is an issue we are aware of and it has been scheduled for a fix.
Regards,
Geez

When I submitted this ticket, I neglected to mention that when this problem appears, I see a "Receiving" message in lieu of a "Wring T-shirt" menu option.

Generally, when I get a "Receiving" notification, this is quickly followed by a "No Message Received" notification. When I experienced this problem, however, I did not receive a "No Message Received" notification, nor was I disconnected from the server.