To break the loop here lol. I take it that you have the screen down and it should resume when you open it or you leave the screen up and use the power button to resume? But, of course it doesn't always even start up physically and when it doesn't you can plug the power cable in and it does, correct?
If so then it sounds like a physical - or at least a software issue for the hardware - and may require the manufacturer fix.
If it were a Windows related issue then it should always at least power up. Now, Windows or a driver could maybe do something on suspend perhaps that breaks resume but the laptop should still power up. No power up should be the hardware or its software such as the BIOS.
You could check if a newer BIOS is available and update it if so. Some laptops also have weird power off special things to reset stuff but you'd have to find if there's something specific for that model. And, probably contacting the manufacturer or getting it repaired or something might be necessary here.
In theory its possible that the battery is bad early or going dead from he low power usage of suspend. I don't know. You seem to suggest it isn't. But, still that'd be a physical issue and impacted by putting the power plug in. The only other way to reason on that is that inserting the power plug runs something else in the hardware's software and starts it up which is going with what I wrote above. But, that also means something is wrong with the battery side of things physically or with its hardware's software.
Now if it does actually physically turn on then it would be a resume/suspend related issue which is completely different.