Are you soaking the patch?A chunk of bear grease........as in a frozen chunk of bear grease. Neighbor brought it over in a large zip lock freezer bag. I put it in the freezer and a few days later when I got it out of the freezer, I cut a smaller chunk off and put the rest back in the freezer. I was surprised to see after the chunk I cut off sat out for a while, it melted into a thick oil as is.
Neighbor said a buddy killed a bear and gave that chunk to him. That's all I know about that frozen chunk of bear grease, other than its slicker than slick. I know not if it has been rendered or not. I used it straight, as is, for a patch lube and the only parts of the .015" patch I found was blown all to pieces. I am, however, in the process of mixing it with different mixtures of beeswax and have actually done so but haven't tested it yet.
I also know its great to apply to the outside of a barrel as well as the stock. But I will most likely not be using it for that, it was just a test. I want to hang onto what little bit of bear grease I have for patch lube recipes.
I never had patches blown out but I only dab one side (patch to barrel side) rub a bit with finger and down the barrel it goes.
Also you mentioned 'cotton' patch...perhaps it is not a good tight weave? I have never used cotton for patches, generally linen or ticking