We have performed time-resolved terahertz absorption measurements on photoexcited electron-hole pairs in undoped GaAs quantum wells in magnetic fields. We probed both unbound- and bound-carrier responses via cyclotron resonance and intraexciton resonance, respectively. The stability of excitons, monitored as the pair density was systematically increased, was found to dramatically increase with increasing magnetic field. Specifically, the 1s-2p_{-} intraexciton transition at 9 T persisted up to the highest density, whereas the 1s-2p feature at 0 T was quickly replaced by a free-carrier Drude response. Interestingly, at 9 T, the 1s-2p_{-} peak was replaced by free-hole cyclotron resonance at high temperatures, indicating that 2D magnetoexcitons do dissociate under thermal excitation, even though they are stable against a density-driven Mott transition.