Perhaps you might have a case of Viagra Dick.  It's happened to me a couple of times.

As soon as the pill starts to work, about 20 min, you need to have sex, even with yourself.

If you wait too long you may not be able to cum.  Used to piss my wife off and was a contributor to our divorce.  I had not idea about it till I was in the hobby.

She explained that clients who take too much sildenafil get very hard but cannot achieve an ejaculation. The key is to start with a low dosage and find the right dosage that works and you are able to cum.

I get my sildenafil in 20 mg. doses and adjust my dose. I sometimes take 80 mg. and sometimes 60 mg.

That happens with me sometimes too. When you get rock hard you may be able to last longer. Many consider that to be medication benefit assuming you do cum eventually. If it's taking too long change positions and/or get some more oral.

Some people simply can't follow instructions!

Personally, I impress the hell out of myself on my ability to get all big and hard at my advanced age. But I can't turn it on and off as desired. Even worse than your scenario, I go over the edge when I'm not so hard. I think I'm jerking off too much. Simple as that?

Or is it that the viagra puts us in new territory. I mean it is likely that stimulation will decrease with time. So if you stay hard longer without cumming then you are getting further into the period of less effective stimulation.

hi everyone .. i think Gnubie is closest to me ...  without viagra ..  if i or my partner starts stimulating me .. i only get moderately firm but would still pop very easily even if i didnt want to.  

with viagra ..i get hard and can last as long or as short as i want .. i have control over cumming ..which of course is much more enjoyable    vs being moderately soft and cumming quickly.    

kinda inverse of what you would expect  ie  hard, cum is controllable  .. soft, i pop fast and cant control.    

men are weird

If I take my usual 20mg of Cialis, I can maintain the Dino Dick™ at full speed for quite some time. However, achieving an orgasm is occasionally elusive, no matter how much she (or I) try.

I've found that "sweet spot" by taking it TWO DAYS prior to our appointment. Then I get 90 minutes or so of full-strength hardness with a 90+% chance of achieving the goal.

Point being, you might need to experiment with timing and dosage to achieve that sweet spot for yourself.

Buena suerte!