Definitions for umpteenth
Random House Webster's College Dictionary
Origin of umpteen:
1915–20; ump(ty), fanciful designation for an indeterminate number
umpteenth, umteenth, umptieth(adj)
last in an indefinitely numerous series
Occurring in a relatively large but unspecified position in a sequence.
That's the umpteenth time I've had to tell him not to swear in front of the children.