To have a shot at answering i think i need to know what is causing you to fail, is it the fed opponents ganking you or are you trying to teamfight with them?Do they simply appear to stop your pushing infront or?`
Different situations require different answers here.
##You are pushing with enemy toplane trying to stop you and you get collapsed on.
You are trying to push but enemy toplaner stuns you or such and fed enemy appears and kills you, to avoid this the only way is wards and ideally having your team pressure another lane so that you´ll have a better shot at guessing what the fed enemy is doing.
Not stopping your team? Likely going towards you.
Stopping your team? What about the others? And so on.
##Teamfight with Tryndamere?
Only do this when exceptionally ahead and even then it´s not certain to work, better to splitpush.
##Fed opponent appears by the tower you are pushing towards?
Seriously depends, if you can beat them 1v1 then do so by all means but if it´s not doable then it´s better to instantly rotate elsewhere while they are clearing minions.
If you are feeling cheeky you can try to walk out of their vision and move to try and ambush them if they follow you but otherwise simply try to rundown some other opponent in the meanwhile or walk to another lane entirely and push that instead and repeat this until you succeed.
Do take care to avoid being caught on the way around if you do not want to fight though otherwise do not stop doing this unless you think a whole heap of opponents are going towards you and you need to escape ASAP.