Wales' 14th successive Test match defeat on Saturday could prove the final straw for Gatland's Welsh Rugby Union bosses.
They have promised a detailed review of Wales' Six Nations performances after the tournament and matters are hardly likely to improve given that remaining fixtures are against Ireland, Scotland and England.
It was Gatland's 20th loss in 26 Tests since returning for a second stint at the helm, an eighth Six Nations reversal in a row and the first time Wales have suffered back-to-back defeats against Italy.
They also slumped to a new world ranking low of 12th, with Georgia climbing above them following their Rugby Europe Championship victory over the Netherlands in Tbilisi.
Rainswept Rome provided a suitably miserable back-drop for a Wales team undone by Italy wing Ange Capuozzo's first-half try, plus five penalties and a conversion from full-back Tommaso Allan.
Wales managed an Aaron Wainwright try and late penalty try, plus a Ben Thomas penalty as Italy had forwards Marco Riccioni and Dino Lamb yellow-carded during the closing minutes.
But there was no reprieve for Wales, with only a losing bonus-point collected and the inquest will be long and hard ahead of them resuming Six Nations action against Ireland in Cardiff on February 22.
It didn't help that Wales suffered a double blow ahead of the game with full-back Liam Williams and lock Dafydd Jenkins both ruled out. Blair Murray and Freddie Thomas replaced them.
"Discipline let us down. We gave them opportunities to kick points and that built the score board to be too high at the end," acknowledged Welsh skipper Jac Morgan.
"Today we showed how practical we can be and how confident we are in what we can do," said Italy captain Michele Lamaro.
"The only goal that we discussed this week was to deliver on pitch for a full 80 minutes."
