An event which happens infinitely many times is not one which continues
unboundedly into the future (either in discrete repetitions or as a single
at-least-half-infinite interval). For example, if there is a light switch
which is 'off' and then I flip it 'on' and back off in a single instant
(point in time) and then wait one second, then similarly flick it 'on' and
'off' and then wait a half of second, and then repeat this process with
the wait between toggling events being halved each time, then I would
repeat this process an infinite number of times even though the whole
sequence of such events would be over by the 2nd second after the first
toggling. All of the infinitely many togglings are bounded by an interval
of duration (exactly) 2 s. An event sequence which is so bounded is not
eternal and does not happen eternally, in my understanding of the word.