Some songs are very easy to learn and remember, other songs take longer. I usually learn a song's intro for example, just the intro, until I have the intro in fluent memory. If the intro is simple, that doesn't take long, it can be memorised in minutes, but if it's not, it can sometimes take days to master.
Then I go back to adding the next phase of the song to what I've learned. Some parts have to be broken down into manageable pieces.
The more songs you commit to memory, the more you will have to practice to keep some from becoming rusty.
If I learn a new song, it won't stay in memory if I don't return to practice it soon, preferably the next day.
I usually learn songs in groups, this is because I read music very slowly, I commit to memory out of necessity (I close my eyes a lot when playing). This either happens if I'm in the mood to learn some new songs, or because somebody buys me a book.
I will only learn 1 song by itself (not in a group) if I've decided there's a particular song I would love to be able to play.
Suppose I get a new book of songs, I will figure out how to play the songs I am familiar with and like. I put post-its in the book to find them quickly. I will find that I enjoy playing only a handful of those songs, and soon be able to play them without the book.
In an hour's session (that's short for me), I can practice about 15-30 songs (I rarely play all the songs all the way through when practising them, some songs I abbreviate to intro-verse-chorus-ending), if I have recently learned some new songs, I will usually play those first, then take a break by playing my favourites, and then return to the set of new songs.
Since I play mostly rock/pop, some songs just don't sound as good as piano solo, or they go out of fashion, so there are a few that get dropped from my repertoire, and I forget parts of those songs over time.
I think songs that you compose (if you compose at your instrument, as a performance), are very easy to learn and to remember.
I don't know if sight-readers have a greater capacity for remembering the music. I suspect they can spend less time figuring out the notes and more time playing, but speed is not capacity.
If your goal is to be able to perform without the music (like a rock star would!) then I guess it's a matter of practising without reading the sheet music.
There was a documentary on the TV years ago about a blind boy (I guess he's a man now) that had perfect recall, he could play any piece just by hearing it once, now I guess that's the level at which the limit basically vanishes. I'm not sure how to acquire that particular skill.