It might be worth checking the tapping points (gamma matching) on the elements which your having issues with?
I once seen a home brew cobwebb which was struggling to find resonance on one band in particular. Long story short, the person who had made it, had cut the elements to the correct size for sure. They had also placed the gamma tap in exactly the right place. But then promptly (in error) fitted the elements back to front when actually assembling the antenna. That very effectively shunted the gamma match points to completely the wrong place. Reversing the elements solved the problem he was having.
People think a Cobwebb is just a load of dipoles bent in a square. Which to a degree it is. But there is much more to them because of the gamma matching setup which is used on each of the elements. If you are using an antenna analyser, note the impedance on the bands that are giving you hassle, if there not 50 ohm, or close to it, then something is wrong.
Those tapping points help create the 50 ohm match. Instead of the normal 75 ohm expected with a dipole. If it was possible to "slide" those tap points up and down the elements, you would witness the impedance changing on your analyser as you did so. Even without changing the overall length of the element itself. Just think what happens when you have something like an Imax CB antenna (dial-a-match mentality), which uses metal rings on a thread at the bottom of the antenna to tune it. When you do that, at no point is the overall length of the antenna itself changed. But depending on where you have those rings, is where you will find the best 50 ohm (low SWR) match.
Now of course, it is highly likely that your elements were already attached when you got your antenna? So there is no way you could have screwed up. But even if so, my first port of call would be a quick check. Just in case the numpty who assembled it made such a simple mistake. You know, off home early for the weekend and all that.