I reckon you have different variant sites in your files. Individual A has SNPs at position 1, 2, 3, after imputation you'll still have SNPs at position 1, 2, 3. Individual B has SNPs at position 4, 5, 6, after imputation it's still 4, 5, 6.
Once you merge them into one file, Individual A will have three missing alleles at position 4, 5, 6, individual B will have three missing SNPs at position 1, 2, 3. Compare the positions in your merged output files with your input files to see whether that's the case. If that's what's happening with your data there are two ways to fix this:
1) rerun the SNP-calling including all invariable and variable sites. In GATK that's -all-sites or -allSites, in
bcftools call that means removing the -v flag (most tutorials have lines like
bcftools call -mv -Ob -o calls.bcf, where -v means 'only report variable sites')
2) if you're sure that these sites aren't missing (may be impossible? they could be 0/0 - reference, they could be ./. - proper missing, maybe deleted, maybe low coverage) you can rerun
bcftools merge using the -0 flag. In this case missing alleles are set to reference (0/0)
Edit: oh sorry, just saw the 'imputed for the exact same sites', are you sure the input files have all the same positions?