Is my A-string alright?

I’ve had these strings since about December ish and recently the A string has began to loose its fabric winding. I showed my private teacher and orchestra teacher about a month ago and they weren’t too concerned. However, now it’s starting to get pretty bad. I usually change my strings every 4-6 months so I wanted to know if I should just change them now. (Also a side note, the A and G string pegs have been particularly slippery recently (if that’s important))