How do you counter this problem where half of your soldiers stay at home base?

I am now on third day in status where I have 9/10 squad members. But the game on third map (don't remember now the map what I chose to go) has turn to be impossible to advance because AI just retreats.

I can push forward from homebase to 2-3 objectives to "Ruins" but then when I die, all my squad members die very quickly and I spawn easily at homebase and there is no one holding enemy AI from re-conquering again everything from "Ruins" to "West Trenches" and then "West Farm".

And I am usually in 1:3 situation where I am the only force in group of AI who actually gets squad push forward by kills.
I have low K/D ratio, just jumping between 4-5 and the record of kills is low too, just 55. But I still find it too overwhelming when anytime of game I check map and I can see that homebase tiles show 5+10+5 and then there are just few guys between my squad and two conquered objectives. And when the enemy of three times larger force kills me, it is like everyone gives up.

I have tried to change the squad size to 0 so I wouldn't have squad, but still most AI soldiers just want to sit at base and wait that I respawn there.

Is there anything possible to do than just try to convince a friend to buy a game and play online Co-Op to get more soldiers on the front line?
As at the start when you were <1000p soldier, AI pushed forward by itself. But now when it seems I am the chief there, no one wants to do anything

A part of the AI is assigned to defend your base centers, another to defend the base borders and the rest to attack. Depending on the map it can vary. If you would have all soldier to be assigned to attack it would be easy for either you or the enemy AI to backdoor.
Take in mind that for the enemy team it's the same logic for the most maps.

Send the savegame files to me at pasi.kainiemi@modulaatio.com, you can find them at %appdata%\Running with rifles\savegames\your_savegame_folder\

You seem to have got lot of XP, so radio calls have been available to you for a while. Did you use any paratroopers at any point? 8-man paratroopers can really help if you feel you are low on soldiers, and using RP to get paratroopers sometimes is nearly required if you're playing on hard difficulty.

Anyhow, I tried Moorland Trenches in campaign by completing & skipping the first maps, ending up with 0 XP in the map. We initially had Hotel (which has got a radar tower which binds 10 defenders in there), we easily captured West Farm from Grays, then the attack was pointed to West Trench, also held by Grays.

I can see that the amount of attackers was very low, probably 4 guys at max, it took a few attempts but we managed to capture West Trench too. The tactic that seemed fruitful (could be a fluke) was that we fought in the trenches, not hugely pursuing to get to the base center, but just focusing on surviving and wasting the enemy resources by killing them there at the spot and not advancing. This took several minutes, and I died in there several times, not saying this happened easily. Finally their forces ran out in the base, reinforcements still probably running from other bases to the spot, and we could easily capture it as it was empty, there was one fellow bot with me to do the capture.

Then we defended it against enemy reinforcements, tried to keep it to us while our defense reinforcements were spawning and traveling there.

The next target was the Mansion held by Browns, when series of captures back and forth between Greens, Grays and Browns started, I found it pretty fun that the chaos was taking place. Also that we lost a base at any given time meant that we still had some leftover soldiers from the previous situation when we had more bases, as capacity follows base ownership. Those guys were useful in getting the bases back again.

Anyhow, the radar tower binding 10 guys can be a problem, and for some maps we've alleviated that by just offsetting all faction capacities by 10. I tried that, and I captured the 4 bases in 9 minutes, so I'm not setting it at 10 for Moorland Trenches, but I'm settings it at something anyway.

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Two times I tried but they just went rambo and got killed because enemy had about 20-25 soldiers coming in two simultaneous waves.

And I spent all the points trying artillery etc to help.

But I have the problem that I don't even have a clue how to get trucks captured, I drive them next to armory but nothing. So I just do that I collect stuff what enemy soldiers drop and return them to armory.

Did google once about the truck drop location but didn't find anything sane and the orders of returning it to armory doesn't help much. But now I don't even much see enemy trucks so I can't even return them, unless I go to hunt them to their bases where I get overwhelmed by them with my 10 man squad (1+9).

Well, maybe it will ease now on as two friends got inspired to buy the game
I still send you the save games.

There can be some bugs with tracking that objective, but in general only Cargo trucks are of interest (not Transport trucks) and only enemy ones at that. The best way to do Cargo truck objectives in singleplayer in my experience is to go lonewolf or take 1-2 squadmates and leave them a bit behind when you go in with suppressed MP5SD to take out the possible enemies near the Cargo truck. Approach it from behind so that the driver won't spot you. Always do it by night.

Cooperative can help tremendously executing them.