Why couldn't the answer be, "Pudieras haber perdido" since it was hypothetical and you didn't actually lose your job?
The imperfect subjunctive in this type of sentence is not commonly used:
Tú podrías haber perdido tu trabajo con esa actitud tan grosera.
You could have lost your job with that rude attitude.
When we have a hypothetical sentence using a si clause the use of the imperfect subjunctive is correct, for example:
Si llegaras tarde todos los días, perderías tu trabajo.
If you were to be late every day, you would loose your job.
Si pudiera ayudarte, te ayudaría sin duda.
If I could help you, I would, no doubt.
But in the sentences in the lesson you refer to we are not using this structure with a si clause. Have a look here.
I hope this clarified it.
Gracias y saludos
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