It was always my understanding that a claimant had to be able to do the activity "reliably" and in a reasonable amount of time. Given that ME is a fluctuating condition, I would always just tick the box that says you can't do the activity at all.
I have never met anybody with any condition who is as disabled as myself (severe ME for 25 years). People with severe ME are more deserving of PIP than most people. Had my only problem been the need to use a wheelchair, or the inability to cut up food, I would have continued in my job as a lawyer. If the DWP is incapable of understanding this, then they are going to find themselves drowning in appeals.
Everybody with ME who is denied PIP needs to appeal. Even if you can't physically attend the hearing. I once won an appeal by writing to the Tribunal, explaining my condition, and explaining the fact that I could not physically attend the hearing.
Several of my friends are judges, and on the whole, they tend to be very reasonable people.