When that happens to me, I try the left hand in isolation (not hammer-ons and pull-offs, just pick the first note and don’t pick the rest. This is just for analysis, not for practice. I often find that I can play the notes fast enough, but the timing is uneven, which causes synchronization problems and uneven volume across notes (unintential accents, dropped notes, unnecessary swipes, etc.).
Then I practice the left hand with hammer-ons and pull-offs. I find hammers and pulls provide improved mechanical timekeeping for the left hand over just not picking. This allows me to sharpen the timing on my left hand, without worrying about synchronization.
Once I can play it in time with hammers and pulls, I try to pick it again. I don’t try to keep the hammering and pulling motions while I’m picking, I just try to play it normally. I usually find an immediate and fairly large improvement. Do this a few times a day for a few days and I’m usually good to go.