Can you get an article 15 for not answering your phone?

Personal phone, I'm guessing. I've heard of it being attempted but it is easily fought. I had a 1SG once threaten to Art 15 me for my voicemail message being "unprofessional". The fact is that although you are a soldier 24/7, your phone is your personal property and in reality you aren't required to have one. If you are required it you would be issued one. Until the military gives you a specific stipend to pay for the phone or issues you one you can not be held in violation of anything for not answering a phone call. If they really want to push for it I would ask to take it to courts martial.

Not answering your phone? Maybe not. Not answering a specific call would probably be difficult to justify for the purposes of UCMJ. People miss calls all of the time (e.g. asleep, in the shower, etc.). However, this may be a bigger issue. Your not responding to a call from the unit can be a major issue, and may very well easily justify UCMJ. Even when people are on leave, the Army can revoke your leave and call you back in to the unit. It's the soldier's responsibility to remain available for contact whenever off-duty, on pass, or even on leave. That's why you have to provide contact information for alert rosters, on your pass form, on your leave form, etc. I even had to do that when on terminal leave.

So, is this simply a matter of you not answering a specific call? Or, is this an instance where you did not answer the call and refused to return the call(s) for the remainder of the weekend? If the unit believes you were purposely avoiding communication with them, simply because you were "off", that very well can justify UCMJ.

It depends on the unit status- it could have be a recall, etc. might take a typing course too.