Troops had suffered weeks of attacks by ethnic Karen insurgents, allied with other anti-coup forces.
Hundreds of troops guarding the vital border town of Myawaddy have now agreed to surrender.
Most of Myanmar’s overland trade with Thailand passes through Myawaddy.
On Friday, the Karen National Union announced that it had accepted the surrender of a battalion based in the town of Thanganyinaung, about 10km (6.2 miles) west of Myawaddy.
It posted a video of its jubilant fighters showing off a substantial arsenal of weapons they had captured.
Over the weekend, the Karen forces have been negotiating with the last remaining battalion inside Myawaddy, which has apparently agreed to surrender.
This is a serious setback for the military junta, which in recent months has also been driven out of large areas along the Chinese border in Shan State, and in Rakhine State near the border with Bangladesh.
Thousands of soldiers have already either been killed, or have surrendered or defected to the opposition, forcing the military to impose conscription on the population to try to make up the losses.
The Karen National Union has been fighting for self-rule for the ethnic Karen people since Myanmar’s independence in 1948.
However it suffered a series of defeats by government forces in the 1990s, and after 2015 had been part of a national ceasefire.
The 2021 coup changed that, with the KNU announcing that the overthrow of the elected government led by Aung San Suu Kyi had invalidated the ceasefire.
Because it is relatively close to Yangon, the largest city in Myanmar, and offers the best route to the Thai border, Karen State was a favoured destination for dissidents fleeing the brutal military suppression of protests after the coup.
The KNU has helped train many volunteer fighters from the cities, who have joined it in renewed attacks on military positions.
The KNU has also been trying to co-ordinate its operations with those of other big insurgent groups like the Karenni Nationalities Defence Force to the north of Karen State, and the Kachin Independence Army in the far north of the country.
The balance of power in Karen State has recently shifted in favour of the opposition, as a powerful militia based on the Thai border, funded by scam centres and which had been backing the military junta, switched sides earlier this year.
Overstretched by fighting in so many other parts of Myanmar, the military has also been unable to reinforce its positions in Karen State, and it lost control of the main roads to the border.
The junta has responded to these losses by launching more air strikes on the areas now controlled by the insurgents.
Thousands of non-combatants have already lost their homes to the conflict in Karen, and many more are now reported to be moving towards the Thai border in anticipation of continued air strikes in the days ahead.