No. At least not for the reason you state.
You're confusing a single compromised user account, e.g. because someone figured out your password, with a compromised application platform. If I get access to your facebook account, that doesn't mean that I get access to the underlying machinery. And if I did get access to facebook's innards, it wouldn't just be a problem for you, but likely for every facebook customer. So while its true that with such access, I could keep compromising your privacy etc, that would also apply to lots of others, so you wouldn't technically be more likely than anyone else to be compromised, and being compromised yourself wouldn't have anything to do with an individual breach of your account.
Of course, if you used the same password on every online service and I found out what it was, then I could compromise every one of your accounts. But I assume that's not what you meant.
Also, if I compromised your mail account without you noticing, I could get continuous access to most your online accounts, even if you changed your passwords on them, because I could use their password reset functionality thanks to the access I had to your mails. But you'd notice sooner or later, because I'd need to change the passwords in order to gain access, so you'd keep wondering why your passwords didn't work.