Hello.  I have a 2009 Honda Civic Sedan, automatic,  with 178000 miles on it.  About 2 weeks ago I accidently drained my battery by leaving my car on while I was eating lunch.  Couldn't start it later that night, even with a jump.  Left in my work's parking lot overnight.  Came back the next morning to call a tow service, went to start it to see if anything happens, lo and behold it starts like nothing happened. Drove it back home.  Tried to start it again later that day, wouldn't start.  Called AAA battery service and they tell me that the battery was fine.  Saw that my cable terminals were loose.  Tightened those back up.  The car takes about 3 tries to start.  Take it to work, starts fine later that night.  Then for the next 2 -  3 days the intermittent starting is happening.  First couple of tries nothing happens then the car starts up like nothing happened.  It has been fine for the past week or so.  Not sure if it's a battery issue or a starter issue.  The battery is 3 years old and the starter was replaced 2 years ago with a refurbished one.  Any thoughts?  I'm hoping that it's just a battery issue.  

Thanks in advance.