What you can do is leave the fabric in place once applied for another hour or two to allow the tacky basecoat to cure further and get a better grip.  If you aren't already doing so, use masking tape to hold the fabric around the corner on the back of the part as this will help too.  Use as much tape as necessary as it won't be seen and can be peeled off when you are trimming the edges.

Warren Penalver
Easy Composites / Carbon Mods - Technical Support Assistant

Hi, so recently I acquired your carbon fibre skinning kit which so far has been working a treat, however on parts that have edges I’m really, really struggling to get the dry carbon to stick round the edges, 100% of the time I just give up. Now I’m looking to do a part that in my opinion must have the edges done, how can I achieve this? Is there some a way to maybe speed up the dry time of the resin to allow me to fix the edges on? Or is it just impossible to do with this kind of part?