Does the risk of getting long Covid increase each time you get reinfected?

...kinda.

The interviewer goes on to ask: "Does that risk add up, or does each roll of the dice stand alone?", referring to whether subsequent COVID infections increase the risk of long covid. To which Ziyad Al-Aly replies: "That's really hard to answer."

He goes on to speculate (his word, not mine) that there can be two outcomes of COVID infections:

• One, that each infection causes some sort of subclinical damage that increases the odds of bad outcomes during new infections OR
• Two, that the immune system may "learn" the disease and lead to milder outcomes in the future.

So in a broad sense, the above TLDR is true because your lifetime odds of getting long covid go up in a way that is vaguely proportional to your number of infections.

But it is NOT proven to be true that number of infections correlates to your odds of getting long covid during any one particular infection.