I am trying to combine several propositions into one sentence without making it sound verbose. Does the below sentence have any grammatical or logical issues? Is it clear? Abigail, who was once my friend, gave me good advice, which sometimes I followed and sometimes I did not, though I always appreciated it.
It is clear. I understand exactly what you mean. I would point out, though, that this sentence has two relative clauses. The purpose of a relative clause is to give extra, non-essential information. Basically, the sentence should function without it. Technically yours doesn't pass this test. (Abigail gave me advice, though I always appreciated it.) So, I would make this change: Abigail, who was once my friend, gave me good advice. Sometimes I followed it and sometimes I didn't, but I always appreciated it.
To keep as much of your original sentence as possible whilst still passing lustrousonion's test: Abigail, who was once my friend, gave me good advice, which sometimes I followed and sometimes I did not, though and I always appreciated it. becomes: Abigail gave me good advice and I always appreciated it.
Personally I'd go for Lustriousonion's version - it's the clearest and easiest to read. Your original sentence, as it stands, is clear. But it's also clunky and not good writing. Because of the sheer number of clauses involved, you end up pausing every few words, which really breaks up the flow of reading. People don't read simply for clear language - people read for enjoyment. If it's not good to read, even if meaning is perfectly clear, still nobody would read it. So I'd think about the flow of a sentence on top of your current good efforts at making your writing less verbose.
I would also go for lustrousonion's sentence, as it sounds cleaner. The original sentence, "Abigail, who was once my friend, gave me good advice, which sometimes I followed and sometimes I did not, though I always appreciated it," contains an appositive (if my thinking's correct), so it should sound like this if you take out the appositive: "Abigail, who was once my friend, gave me good advice, though I always appreciated it."----> "Abigail, who was once my friend, gave me good advice, and I always appreciated it." The first sentence doesn't really make much sense, so it'll be nice to split up the sentence as lustrousonion did. Or you can just do the "and" thingy, like Shadowfax said. Personally, I would go for the "splitting up the sentence" thing.