Look at this (on a Windows, New York-time, computer):
> as.POSIXct("1970-04-26 01:59:59",format="%Y-%m-%d %H:%M:%S")
[1] "1970-04-26 01:59:59 EST"
> as.POSIXct("1970-04-26 01:59:60",format="%Y-%m-%d %H:%M:%S")
[1] "1970-04-26 03:00:00 EDT"
Depending on your locale, it seems on 1970-04-26 there is the switch to Summer time, and there is no 2 am (the entire hour is just skipped). This disappears if you specify a time-zone:
> as.POSIXct("1970-04-26 01:59:59",format="%Y-%m-%d %H:%M:%S", tz="UTC")
[1] "1970-04-26 01:59:59 UTC"
> as.POSIXct("1970-04-26 01:59:60",format="%Y-%m-%d %H:%M:%S", tz="UTC")
[1] "1970-04-26 02:00:00 UTC"