Piano Forum

I don't think learning is always so linear.  Often there are technical hurdles in learning a new piece that can make progress slow, and these hurdles are often the sort where you can play something at a moderate tempo but things break down when you try to play a piece at its designated tempo.  So it feels like you're making only tiny progress, but once those hurdles are surpassed learning can accelerate.

I'm an adult learner, and at times my schedule has been such that I haven't been able to have a teacher.  Having a teacher is the most helpful thing when you're learning a difficult piece.  K545 was my first sonata, and, like you I could play it slowly, but playing the first movement allegro gave me all sorts of issues.  What I did was put it on the backburner and learned more attainable pieces, while practicing the parts I had problems with on a daily basis.  It's really a cornucopia of intermediate technique, with trills, cantabile playing, scales, passagework, tremoli, and arpeggios, so there can be a lot to work on.

The most frustrating part to me were the scales in the piece, because they have to be fluid and smooth, and subtle dynamics really transforms them from sounding mechanical to sounding beautiful.  I'd thought my scales were ok, but they weren't.   What was the most help for me was rhythm practice.  At first do one rhythms, which is a long note followed by a short note or vice versa.  Then do two rhythms, which is a long followed by two shorts, or two shorts followed by a long.  What helped the most for these passages were 5-rhythms with four short notes followed by a long note.  So if you're having issues with the scales near the beginning play the following:

ABCDE (fingered 12312) fast, holding the E a moment
then FGAGF (34543) fast, holding the second F a moment
then EDCBA (21432) fast, holding the A a moment
it just falls where it should, so then you can do the same thing starting on G, do that, do F, E, and get down to the D.
I practice it with a slightly detached nonlegato.  With this kind of practice you can also hear where you might be uneven.  Start a little slow but work up to tempo.   When I first started this method I had two issues.  The first was unevenness in thumb crossings especially on the descent, so I had to slow down and focus on dynamics, and bring it back up.  The second is fingers 345 which have the top notes of the figures.  They are very interconnected fingers and weaker, so it took a bit of practice to get them fluid.  Once I could do the 5-rhythm fast I knew I could actually play the passage at tempo (and beyond), and it mostly becomes an issue of putting it all together, i.e. getting rid of the long notes in the 5-rhythm.