All the dictionaries say this is a perfective verb. I wonder if it's both perfective and imperfective, in other words is it possible to say (excuse any errors) something like:
Я продержусь ради моих детей.
I'm holding out for my children's sake.
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Sign up to join this communityI'm holding out for my children's sake would be
Я держусь ради моих детей
The verb продержусь is indeed perfective.
Я продержусь ради моих детей
This is actually the Future tense, it means "I will (can?) hold out for my children's sake".
продерживаться probably exists, but might not be formal. Almost all verbs have both perfective and imperfective, even if dictionaries say they don't exist. Just search on Google for the usual form, and 99% of the time someone has used it.