Joni Ciarletta writes

You are not alone.  My '79 Honda Accord with 110,000 miles on it started  
showing the same behavior.

I replaced the brake master cylinder myself.  It took about an hour and cost  
about $45.  Sure beats paying $300 to have someone else do it!  If I wanted to  
rebuild my own master cylinder instead of putting in a rebuilt one, it would  
have cost only $20 to $30 for the rebuild kit.

The Honda brake master cylinder is easy to get to.  Two bolts attach it to the  
engine compartment.  Two brake lines enter the master cylinder.  The tricky  
part was that the brake lines were stuck tight.  My Craftsmen open end wrench  
rounded off the bolt heads!  I had to use Vise Grips to loosen those suckers.   
Wow!  Best invention since sliced bread.  After that it was very easy.  Bolt  
the new part in place, add new brake fluid, and bleed the brakes.