I don;t know what the airlines legal obligation is if you bought two separate tickets that are not in conjunction. In might be that the airline is not legally bound to transfer your baggage to another airline when the two tickets are not conjuncted.
In case of a single ticket using multiple airlines, an airline that refuses to check your bags through is violating terms of tariff, provided any of your layovers is not more than 24 hours.

An interesting situation arises when you have 24 hours and 10 minutes layover. For example, when you arrive at 9:00 a.m. your next flight departs at 9:10 a.m. You can't very well catch it the same day, so you have to catch it the next day. Your halt exceeds 24 hours.