The short answer to your question is yes it can become resistant. However, given enough time, so can most bacteria too.
The long answer is more complex. Lyme is particularly adept at not just adapting to your ABX like most bacteria, but also resorting to a cyst or biofilm form that is entirely/partially immune to ABX. Lyme also likes to hide deep within your tissue, cartilage and joints, where ABX also has a tough time getting to. All of these factors mean that Lyme needs to be handled differently, with multiple ABXs or herbs or methods. A good LLMD or Lyme expert is key for understanding this (and what separates them from the crappy Infectious Disease doctors)
In your case Amoxicillin targets the cell wall of the Lyme. So this helps eradicate Lyme in the blood or when Lyme is in its typical cell form. However, if the Lyme switches to a cyst "survival" form, Amoxicillin is not going to touch it.
Post Edited (vcast) : 1/14/2014 3:35:26 PM (GMT-7)