So this really is a situation where there is no way the EU would cut off it's nose to spit it's face on this one.
This is not the issue. The EU will have rules and regulations with the how system is run. It will be enforced through some sort of authorising body probably with the European Court of Justice as it's legal backstop.
The UK is leaving and as such we will cease to be bound by the laws which enable the system. The EU cannot legally allow us access if we are no longer bound by these regulations. It is possible that the laws and regulations can be rewritten and agreed to allow for the UK to continue participating.
But this will take time, that is what the transition period is for. If the UK leave without successfully negotiating a withdrawal deal there is no transition period. We become a third country that the EU both by it's own laws and international laws needs to treat like any other third country.
I've been a bit vague on the specifics as this issue is replicated across practically every single sector/industry. The EU is a rules based organisation it cannot simply change its rules on a whim. It takes time and agreement to make these changes.
This is why the whole "No deal is better than a bad deal" spiel is a load of rubbish. We're supposed to be negotiating an orderly withdrawal.