Should I be patient with this postdoc application?
So, I am wondering if this is the norm, if this happens sometimes. or
  if this never happens [and I should forget about the job


Yes, this happens. I have been in the exact same situation myself: application, shortlisted, interview, informal acceptation by the PI, but then the formal confirmation was postponed several times over a couple of months. This doesn't depend only on the PI, sometimes the administrative process gets stuck somewhere. I wouldn't say that it's the norm but it's not uncommon.

As long as the PI answers your emails and confirms that it's in progress, It's likely that you are going to get the job. It would be unwise to take it for granted though. Keep applying for other positions, and don't close other doors as long as it's not confirmed. From time to time, email the PI; in particular you should ask when the contract is supposed to start, and try to politely tell the PI that you cannot wait forever; if you have other job offers waiting for an answer, you can mention it, it might speed things up.