#They can use it every time they die

You have quoted the relevant section and the only place where the ability is described.

At the beginning of Psionic Body it says:

You gain the following benefits: [...]

There are no conditions on the benefit so you gain the benefit unconditionally. Psionic Body has no limit or any other restriction on how many times they can be used if it did, it would say so.

Thus, every time a character "dies" they roll a d20 to see if they actually do.

They can use it every time they die

You have quoted the relevant section and the only place where the ability is described.

At the beginning of Psionic Body it says:

You gain the following benefits: [...]

There are no conditions on the benefit so you gain the benefit unconditionally. Psionic Body has no limit or any other restriction on how many times they can be used if it did, it would say so.

Thus, every time a character "dies" they roll a d20 to see if they actually do.