Donna O'Halloran said her son David had consumed a large amount of alcohol in a short space of time shortly before he vanished.
It came as the police search for the Stirling University student entered a 13th day, with a helicopter called in as searches of gardens continued.
Mrs O'Halloran issued her plea on the Please Help Find David O'Halloran page of the website. She said the fact the first year Stirling University maths and education student had been partaking in drinking games had not yet been mentioned in reports.
The 18-year-old, who previously attended Stewarton Academy in East Ayrshire, was seen getting into a cab near the popular Dusk nightspot in Stirling city centre, at around 12.30am on January 18.
He was then seen to walk along Airthry Road from Causewayhead at about 1.15am and was seen at the roundabout outside Stirling University at 1.57am.
Staff at Graham's Dairy saw him and pointed him in the right direction for the university but it is understood he decided to wander in the opposite direction.
Mrs O'Halloran said: "Points that have not been mentioned are that the same taxi driver had also seen David on the scrub side of the roundabout at the entrance of the university at approximately 01.57 while dropping of students in the university and the drinking games that David played before going out.
"I know lots of young people now play drinking games – I well remember being young and invincible. How I am still alive I don't know. Large amounts of spirits in short time periods or spread over large periods can kill.
"It can affect your kidneys or liver beyond repair. Please calm these games down. You have all your lives to live. Add in some glasses of water or juice."
David is 5ft 5in tall, of slim build and has brown hair, with blond highlights, which is short at the back and longer on top. He was wearing a white T-shirt with a black and green checked shirt on top. He was also wearing black slim-fit jeans and black trainers.