The 20-year-old joined Town in mid-August on an initial month-long deal and has impressed enough to have now prolonged his stay up until the maximum 93-day period allowed.
Reach has so far made 10 appearances for the Shropshire outfit, scoring once on his debut in a 2-0 win over Swindon.
Manager Graham Turner told the club's official website: "It was fairly straightforward. It was a setback obviously for Adam not to be in the starting line-up last Saturday (against Gillingham) but he realises he's had a lot of game time here.
"He had started the previous four games and had a good hour on the pitch at Bristol City so he's had some valuable Football League experience and there's more to come in the next month."
However, there is disappointing news for boss Turner with confirmation midfielder Luke Summerfield faces a couple of weeks on the sidelines due to injury.
Summerfield missed last weekend's 2-0 victory over Gillingham due to a groin problem which is set to keep him in the treatment room.
Turner added: "He's looking very doubtful for a couple of weeks. He's tweaked his groin so he certainly won't be in contention for Saturday."