Originally Posted by
wcj1
The general rule is that a domestic connection is limited to 4 hours or the next available flight (you can find this in the fare rules for the particular flight you are booking, but it is pretty much boilerplate). So if this is a domestic connection and you want more than 4 hours, the system will then generally price it as two one ways, which is often more expensive.
(Edit: pulling a fare rule excerpt)
STOPOVERS
NO STOPOVERS PERMITTED ON THE PRICING UNIT.
NO STOPOVER OCCURS IF PASSENGER TAKES NEXT
AVAILABLE FLIGHT WITHIN 4 HOURS.
(Looks like they took out the next available flight provision. I honestly haven't looked at this part of fare rules in forever.)
Those are not the stopover rules for BQN fares. While most US48 fares don't allow for stopovers, fares to Alaska/Hawaii/US territories will often have provisions to allow them for an additional fee. In this case, BQN fares allow them for an additional fee of $150 (it's waived for infants under 2). The other way to book them is as broken fares where you have a separate fare on each segment (this can be done using multi-city). Sometimes, cheaper fares don't allow for end-on-end fare combinations (unless they are roundtrip A-B-A style routings) as airlines may want to only allow more expensive through fare options. But this does not look to be the case here and it looks like broken fare combinations are cheaper in most cases than booking on a single fare and paying the stopover fee.
Example of ITA constructing broken fare combinations (as they are likely cheaper than a single fare with $150 stopover fee).