The promise is not to learn to tolerate abandonment -- it's to learn that not every separation is abandonment.

It's not abandonment when you don't get a text or email back.
It's not abandonment when your therapist goes on vacation.
It's not abandonment when your therapist doesn't see you every day and isn't always there.

Just because it feels like you're being abandoned does not mean that you are being abandoned. The person feels abandoned because of things that happened in their early developmental years. The idea is to experience a healthy human relationship where the therapist, unlike the person's parents, is not abusive and holds steady boundaries that are predictable. You experience -- many times, over time, that a person's not being right there all the time doesn't lead to abandonment.