There's a simple answer as others have stated.
If you can do contract work then there isn't a problem. You work when it suits and don't work when it doesn't.
As for having a full time permanent position, ask yourself the question: would you employ someone who is going to be here today, gone tomorrow and back again 3 months or whatever later and then repeat the process?
The answer for most employers will be a resounding 'no' and it isn't really a difficult concept to understand their position.
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