When you say

« Tu n’as pas perdu cette capacité. »

you are expressing a binary concept, you either have or have not lost the ability. Hence, the de is not necessary. In English, you would say: you have not lost this ability

Saying

« Tu n’as rien perdu de cette capacité. »

on the other hand, means the person has lost none of the ability, translated in french as rien de cette capacité

I’ll try to be clear. The idea behind ‘Tu n’as rien perdu de cette capacité’ is that you ‘divide’ the capacity in multiple parts and you say you haven’t lost any part of it. You didn’t lose 50 % of this capacity, not even 20 %. You haven’t lost anything of this capacity.

At the affirmative form, ‘Tu as un peu perdu de cette capacité’ would mean you still have the capacity, but you lost a bit of it, while the opposite of ‘ne pas’ would be ‘Tu as perdu cette capacité’.

It’s easier to understand if you think about a dish with rice, pasta, meat, vegetables… and you says ‘tu n’as rien mangé de ton plat’. It means you didn’t even eat some of it, while ‘tu n’as pas mangé ton plat’ can mean that you didn’t eat it at all or that you didn’t eat it all.

Of course in the negative form, in both cases you still have 100 % of the capacity, since ‘not losing the capacity’ and ‘not losing anything of the capacity’ are the same.

EDIT :
I’ll try another explanation.

There is a bowl with many M&M’s. Someone tells you:

Tu n’as rien mangé de ces M&M’s.

… it means literally that you didn’t even eat one of them.

If he says:

Tu n’as pas mangé ces M&M’s.

… it means that you didn’t eat them.

But you could say:

Tu n’as pas mangé de ces M&M’s.

… it means exactly the same thing than the first one with ‘rien… de’. Because it’s ‘de’ that implies the notion of ‘from something’, ‘among many of them’.