急に => quickly; immediately; hastily; suddenly; abruptly; unexpectedly ~ N4
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
~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1