If I previously failed to follow up with professors, are they likely to remember this and hold it against me if I ask them for advice again?
You should not fear this. Faculty are very interested in students who will learn, do, and advance. However, you must "do" in order for them to believe you.  In university/college, things are earned and not given.  

Be at ease with faculty.  Speak with them.
This is school. School is a place for learning. Asking for help is not a sign of weakness; It is expected; It is rewarded.  

I have been college faculty (part-time) for a few years.  I know that sometimes student (or anyone) might have a bad day, week, or quarter/semester.  If they are nice, committed, honest, and willing to do something to prove themselves, I'm willing to give them another chance.  (But chances are limited.)  

In some cases faculty just plain forget students. Faculty might have a regular FT job external to university (even full time faculty sometimes have FT jobs).  They might have 40 students in each of 5 classes each quarter/semester.  Too many to keep track of. 

Faculty might also suggest a student followup with them, but they don't expect it.  For example, you ask for help on a paper, and a different prof gives you help and says "Let me know what grade you get."  They likely will not hold it against you.