How long have you been practicing that grip, and how long have you been practicing bottom dealing?
Generally speaking, when you first begin the long road to the bottom deal, this is the first problem you encounter. Your issue most likely does not involve the strength nor the size of your hands, and the size of your hands is not why you have trouble maintaining the grip. When I began, I couldn't even see how it was physically possible for the deck to fit into my hand like that, much less maintain the longitudinal pressure that bottom dealing requires.
I persevered because I had seen my friend with very small hands execute a mechanics grip bottom deal, so I knew it was possible regardless of hand size. For me, it took about two days of just sitting on my bed for hours putting the cards in that grip, trying to loosen the card, having all the cards fall on my bed, and repeat. After a week, I could loosen a card. After two, I could remove a card. It wasn't until about a month in that I could do any semblance of actually dealing from the bottom, and I am still trying to make it invisible (It's been about seven months now). I have practiced either 2nds or bottoms for one hour, every single day since I began over the summer. I have missed two days so far. I am still very, very far away from having what I would call a good bottom or second. Point is, it is a long, long road. There is not immediate gratification, and there are gonna be a lot of cramps and exasperating days along the way.
Also, practicing with a packet of only 35 cards or so will make the move notably easier to execute. It is not a bad idea to begin that way, just ensure that you are also practicing dealing with a full deck so you don't limit yourself.