Don't try to hold things in the early game, build a stockpile of equipment, do missions to gain support from the cities as they give more HR and money income so you can have more AI.

Invest is some AA trucks and position them tactically to cover the airspace around what you want to capture.

Usually a tactic change is all that is needed to solve this issue.

Do multiple rounds of capturing zones. The first time you want to focus on identifying the location the QRF is being launched from, what direction they approach through, and what assets are being used for it. Do not try to actually defend from this QRF, as you are likely not going to be as well prepared as you could optimally be. Once you have identified the assets and their approach paths, then wait for them to retake the zone and the QRF to go away.

Then, focus on preparing for that QRF. If they have a number of APCs/Tanks, place anti-tank mines along paths that they took, are likely to take, or are going to have to take to assault you when you are defending, as well as gather the AT launchers you may need to deal with them, and scoping the location the AT launcher should operate from (ie a nearby hilltop they set up on).

If they have a lot of gunship support like you mentioned, be prepared to requisition some emplaced AA in the zone as soon as you capture it. AI is quite effective at manning emplaced defenses, so you can place a few emplaced AA and hire some AI to man them while the players focus on taking out tanks/apcs/infantry. If not using RHS, AI is also pretty effective at using the vanilla game handheld AA launchers. A key part to this is that if the QRF has both ground and air forces, they are likely going to arrive at different times and via different paths, allowing you to deal with the air forces before having to worry about the ground forces. You can also ambush them along the path they take to reach the zone you captured, you don't have to defend the actual point itself if there is a better point at which you can engage them.

You also don't need to successfully defend the captured zone even on the second time you conquer it. Blowing up enemy assets like tanks and APCs is an objective of its own. Even if they retake the zone, if you kill a tank and a chopper, that's still a successful operation - You are a guerrilla group, and the opposing forces then have to replace that asset you destroyed. Do it enough and they'll start to have some asset shortages, making their QRFs weaker.