Right then. I had the calipers from my front brakes serviced before Christmas & when I put them all back together I couldn't get a firm pedal. After a lot of bleeding I could get it to firm up but only near the end of the travel & the test drive was not a happy experience. To get the car to stop I had to pump the pedal 4-5 times each time.
I got a length of clear plastic 5mm tube & ran it from the caliper back to the master cylinder (the fuid in the system was completely new by now) & pumped the brake pedal. The driver side coughed up a couple of bubbles then ran clean. The passenger side produced a bubble with every pump for several minutes & never ran out of bubbles.
These calipers are Austin Princess type each with 3 bleed valves (I bled from all 3).
So could there be something up with the caliper that is allowing air into system? Would it be entering through the piston seals? There doesn't seem to be any obvious leak.
I'd appreciate any wisdom before I take the caliper back to the reconditioners.

Never say die. At least not while you're still breathing.