To the best of my knowledge, there's no theoretical bottom limit to the speed of an internet connection, although individual programs may give up after a period of time, and assume that the message they were trying to send has been lost in transit.\n\nTo illustrate this, I've linked the (as far as I know, unused) proposal for transmitting IP packets (one of the fundamental units of data on the internet) via trained pigeons.\n\nWhile the attached proposal is certainly geek-humor, I hope it illustrates my point - as slow as your net is, it could always get even slower.
What is the slowest possible internet speed?