To rincon is to habitually decline every invitation to do something no matter the circumstance. This includes, but is not limited to, social events such as lunch with coworkers, drinks at a bar, camping, sporting events, or anything else with an invitation that could be declined.
"Jack is rinconing today and doesn't want to go to lunch."
"Hey, don't pull a rincon today and skip the bar tonight."
"It's margarita Wednesday! Don't tell me you're going to rincon and skip it."