How does meiosis ensure that the chromosome number in each cell remains constant in each generation?

The first thing to know is the difference between a chromatid and a chromosome.

Next, let's look at the basics of chromosome numbers in mitosis.

So it's more or less straightforward in mitosis:

The chromosome number remains constant (46 total chromosomes or 23 pairs of chromosomes).The chromatids replicate during interphase to produce a total of 92 chromatids, but they're only found in pairs and remain connected at the center by the centromere. After mitosis, the chromatid pairs separate, so each daughter cell gets 46 chromatids.
Now meiosis is tricky. Meiotic cells undergo a more complicated process to ensure the correct number of chromosomes.

Here's what happens:

At  first the cells have the same number of chromosomes as mitosis. DNA  replication occurs, giving a total of 46 chromosomes (or 23 chromosome  pairs) and 92 chromatids (or 46 chromatid pairs).Meiosis I: In meiosis I, the homologous chromosomes separate.  In this case, the pairs of sister chromatids are still attached to each  other. So at this stage, the daughter cells get 23 chromosomes each (of  the pair of homologous chromosomes) and 46 chromatids in total (which  are actually 23 pairs of sister chromatids attached at the centromere).  This is known as reductional division, as the total number of chromosomes is halved at this stage. Meiosis II: Meiosis  II follows the same division as mitosis, except that there are only  half as many chromosomes. So the 23 chromatid pairs from the previous  cells (or 46 chromatids in total) split equally, so each daughter gets  23 chromatids exactly, which correspond to 23 chromosomes. Meiosis II is  known as equational division.
So to summarize, in mitosis, the total number of chromosomes is unchanged in the daughter cells; whereas in meiosis, the total number of chromosomes is halved in the daughter cells.