2008 Honda Civic Air Conditioner

I have a problem with the air conditioning in my 2008 Honda.  It will work for anywhere
from half-an-hour to five minutes after I start the car but then kicks out.  One leak was
found last summer and was fixed but the problem continued.  Now I'm being told I
need a new compressor or possibly a compressor coil but mechanic said he wouldn't
fix the coil alone - I'm not even sure if he said he knew which it was for certain. He's  
pricing the job at about $1000.00  I know nothing about AC and very little about cars -
I won't be fixing this myself. I do know compressors are expensive.  Does the
diagnosis sound right?