Factory unlocking question

You have to ask people that do actual unlocking

 

If it's an actual factory unlock - i.e. The carrier the phone is locked to putting it in their system - then no, it will not re-lock.

But "one of these unlocking companies" may do any number of unlock types, not necessarily a true factory unlock.

Note that the only truly guaranteed unlock is one performed by the carrier the phone is locked to - and they will only do it once the account the phone was bought with has satisfied its contract (either through completion of the contract period, or the payment of an early termination fee.) Any other unlock, even if it uses the "factory mechanism", may run afoul of the contract obligations the account the phone was bought with. If that account become delinquent, it is perfectly within the carrier's contract to lock and disable the phone until the account is brought current and/or an ETF is paid.