It didn't take me that long, well, not as long as others. From start (first contact) to finish (initiation), my process was just over 4 months. I knew that I would be invited to pledge Alpha Phi only three weeks after I first contacted them.
Like Jill said, if you contact groups during their inactive period (like summer) or during holidays, it might take a little bit longer. Also, while some (inter)national organizations are very supportive of and open to alumnae initiation, the final decision rests with the local chapter -- and they might not want to do it (and leave the PNAM hanging)
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I can understand being cautious about who you bring in as an alumna initiate, but c'mon -- during recruitment, you're supposed to know everything about a woman in a week or 10 days, and at the end of that she's given a bid. Sometimes it seems that alumna initiates have to "earn" their letters, especially if they're coming in as unknowns.