For soft, adjustable, with a firm connection, that won't hurt when you fall or kneel on it, you really only have one option: sew-on hook and loop fasteners. Any other fastener option is going to be hard, with the exception of using laces with buttonholes (not grommets, which are also hard), but you've also specified issues with using laces in your post, and I do not know if you are comfortable with sewing buttonholes. Additionally, for a piece put under tension like a knee brace, anything other than the laces is going to be prone to separating under stress. In the case of the punch-in snaps you mentioned, they will often tear free from the fabric under tension, damaging your brace; in the case of the self-adhesive and iron-on hook and loop products, they will similarly detach under the tension needed for a brace.
There's a reason commercial knee braces tend to use hook and loop fasteners, and that's because it's the best tool for the job.
As you didn't offer any information on how you're constructing your brace, it's hard to know why you're having trouble, other than your description of using "small patches." The smaller a piece gets, the more challenging it is to stitch in place, and with hook and loop, smaller pieces also have less grip. Your best option to solve all of your issues is to use larger pieces, which will both be easier to sew down, and will have a greater grip strength when closed up, thus offering greater support for your knee.
If you are constructing a fairly standard brace with straps that wrap around the leg to hold it in place, you may want to consider double-sided hook and loop (branded as Velcro One Wrap), which could be used with very minimal sewing, as it would take the place of the entire strap. This material is designed with the hooks on one side and the loops on the other, so that it will stick when wrapped around itself.
Remember as well that when you are adding whichever form of hook and loop you choose, to always have the hook portion positioned to face away from the body, to avoid discomfort from any exposed hooks. Ideally, you would also set the strips within the borders of the fabric, as the edges can also be stiff and uncomfortable against the body.