切る => Give up, stop... N3
Happens next
切る/切れる/切れない => to do something completely to the end/unable to do; too much to finish/complete N3
[切「き」]れない => Can't finish/complete A N3
Potential, Possibility
て仕方がない/てしょうがない => can't help but; very; extremely ~ N2
~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1