Machine-to-machine (M2M) communications being pivotal for internet of things (IoT) networks are characterized by low-cost, low complexity, and often energy constrained terminals with low traffic duty cycle. Satellite networks provide an attractive low-cost solution for such application, in particular when the terminals (both fixed and mobile) are distributed over a wide geographical area not well served by terrestrial infrastructure. An ALOHA random access (RA) scheme is a natural candidate for M2M communications since it is well matched to sporadic traffic, and it requires little terminals coordination. However, the classical ALOHA scheme suffers from a low throughput when operated in a load region requiring low probability of packet loss. To overcome this intrinsic ALOHA limitation, in the last decade, a lot of effort has been devoted to the investigation of evolutions of the ALOHA scheme reducing the probability of destructive packet collisions thus making it more attractive for satellite IoT. In such context, the Contention Resolution Diversity ALOHA (CRDSA) scheme and the Asynchronous Contention Resolution Diversity ALOHA (ACRDA) have emerged as promising solutions thanks to their high spectral efficiency achievable with low packet loss probability. The results reported in literature are however assuming ideal demodulator performance. This paper investigates the design and optimization of RA burst demodulator algorithms for single-frequency and multifrequency CRDSA and ACRDA. It evaluates the performance of such algorithms in a number of system scenarios of practical interest and studies the impact of relevant system parameters on several performance metrics.