On average is about 1.5 pieces a week but recently I am having difficulty maintaining that. The rule of thumb that my instructor and I use is, if it takes more than 1 month to complete the piece, it's just way too difficult for me, It would be more beneficial learning easier piece with less technical difficulties and build up my skill gradually. If you look at my repertoire
https://www.geocities.com/gasilem/musicbooks.htm you might be able to understand how I did it.. the pieces are gradual increment of difficulty, meaning my pieces are just slightly more difficult than the previous piece. Conceivably, you will never ever hear my pieces being performed at Carnegie Hall

. My instructor chose all the pieces for me, there is no way I could do it on my own.
At any one time, I have 3-4 pieces to work on. It takes from 1 week to 3 weeks to finish each pieces, occasionally I take more than a month but its not because the technical challeges overwhelmed me but because the piece is way too long (5 pages)
It's conceivable that a beginner might take a few months to learn my recent pieces... on the otherhand, an advance player like my teacher, could sightread it at performance tempo, complete with expression, pedaling, complete dynamics, phrasing.. everything.. the whole nine yards. I had to see it to believe it.. I am sure many of the advance pianist here could do the same. and I am sure one day I will be able to do it too.
Don't be impressed.. I have a good instructor and both of us work very hard.
i may be thiknig wrong, but i am extremely impressed that you can learn a song in a week. i mean, how hard is that song?? are you talking like an etude (which took me like a 1/2 yr to learn #12 op 25) or like a song w/o words from mendel. ? when i was a freshman in HS it took me nearly a yr to learn and "perfect" fantasie imporomptu. is this too much time?