The number of instances of coin flip seems to be capped by your stats somehow. If you use the coin and the number of instances you know is less than the cap, you get more copies of the technique to bring you up to the cap.
11 (12)/8 (10)/6 (7)/8 (11) gave 2 instances
~20s/?/?/26(20) gave 7 instances
?/?/?/61 (64) gave 11 instances
99 (102)/95 (99)80 (85)/84 gave 16 instances
136/?/?/165 (317) gave 20 instances
384 (518)/184 (178)/187 (178)/185 (191) gave 47 instances
11/8/6/8 = 2
13/9/8/10 = 2
14/10/9/10 = 2
The last two data points here makes me thing that it's perception based. Looks like it's base stats, or at perhaps just once a day. Buffing my stats a bunch didn't seem to help at any rate.
(Thanks to Barton26, Arkaim, Erenoth and PenguinPyro for testing - if anyone else wants to help test, let me (Al) know and I'll loan you my coin)