Do the four cells produced by meiosis each divide into four cells again?
No, meiosis is not a cycle like mitosis. In mitosis, haploid or diploid cells divide to create two genetically identical cells, and this process can go on and on. On the other hand, meiosis results in 4 genetically unique daughter cells which are also haploid. If a haploid cell was to try to undergo meiosis, there would not be enough genetic material and you would end up with half-chromatids.