My 1377 was holding air intermittently which I thought was possibly due to a defective pump seal. Lubricating it seemed to help but it was not a propper solution. So before Christmas I ordered up a seal kit. Never taken a pump up appart before so had a look at the parts diagram & got a pretty fair understanding of how they worked before getting down to actually taking it to bits.
All came apart pretty easily, trickiest bit was removing the circlip on the pump pivot so that the cylinder wasn't marked by something. Anyhow it came off without causing any damage. The pump slid out without a sound, no suction noises or pop as it came out, so fairly sure my suspicions were correct about the pump seal being the culprit. l cleaned things as they came off, popped them all in a clean plastic tray as I went. Took the old seals off the valve, seperated the two halves of the valve took off the washer/seal between them & shook, the bits out of the valve.. grungy, sticky horrible mess in there. Suppose all that pump lube had yo go somewhere!
Cleaned everything up rebuilt the valve, put it all back together, could feel compression ahead of the pump when sliding it in, so began to feel optimistic it was sorted. Popped the pump pivot circlip on, one pump ok, second pump hiss, whoosh, less confident...... tried it, no air stored. Ok cock it first, same result!

To bits again, nothing obviously wrong, back together, left the circlip off this time, still not holding air, pumped ok first held air,second fealt ok till the end of the stroke then hiss...
Appart again let's look at the valve stem seal, looked ok, thought about lapping it with some metal polish, seemed ok cleaning it up noticed a grain of something greenish, same colour as the seal on the valve stem. Closer look & yes the valve stem seal was disintegrating. Being soft it looked ok initially as it bedded to the mating face but it wasn't up to the job anymore. So I dug it out, no valve stems easily or quickly available or seals so it was either going to stay like that or I set about making a seal.
It seems the recommendation is that the brass cup be sweated off the steel valve stem first then a new seal fitted, guess the steel stem is then driven back in. But as I hadnt got a seal I didn't want to risk messing things up any more by doing this. Found some nice tough sheeting .06t thick, cut a disc out of it then took out the centre, pushed it down over the val e stem over the retaining flange & seated it down. Valve back in frame, all back together & hoorah!

No idea how long it will last but valve stem seals can be replaced fairly easily without having to part them.