"Stay X for Y consecutive hours"

[Guest]

Stammerer - Stay silent for 4 consecutive hours.
Quiet - Stay silent for 24 consecutive hours.
Silent - Stay silent for 48 consecutive hours.
Speechless - Stay silent for 76 consecutive hours.

What exactly does consecutive mean? It sounds like staying online X hours without going offline for just a second or getting a disconnect and so on.
But then it would be impossible in Germany since every ISP forces a disconnect every 24 hours. It doesn't take a sec to reconnect but then you have a different IP.