The Leicester midfielder arrived at the Memorial Stadium on 12th January and made his Rovers debut when going on as a second half substitute at Dartford.
He made his first start for the club last Saturday, against Lincoln, when he won the Man of the Match Award.
“Of his additional month, Dawson said; “I’m delighted to be staying at the club for another month and looking forward to getting some more games under my belt.
“I’m really enjoying my time here and was pleased to get my first start for the club last Saturday.”
Manager Darrell Clarke said; “Adam has done very well in the month he has been with us and has worked hard in training since his arrival.
“We have only played three games since he arrived, but he did very well in the game against Lincoln City last week and with six games to come in the next month he has an opportunity to challenge for a regular place in the side.”
Adam will now be available for the games against Grimsby Town, Altrincham, Braintree Town, Gateshead, Eastleigh and FC Halifax Town.
In another loan deal completed this morning, striker Jamie Lucas has returned to Weston- super Mare for his second spell with the Seagulls.
Jamie, who has also spent time on loan with Gloucester City this season, will remain at Weston until 14th March.