I agree, fixation can make things more manageable. Important to wash away FAM peptide non-specifically bound before fixation. I'd add a quenching step with any amino acid or with Ammonium Chloride at 50-200 mM concentration to avoid non-specific staining. I've never done FACS with a sample fixed more than 24 hour ago.
14. Resuspend pellets with 150 μL of wash buffer. Store at 4°C in the dark until ready for data acquisition, which should be performed within 24 h. Optional: resuspend pellets with 150 μL of 1% paraformaldehyde in PBS or BD Stabilizing Fixative (see Note 16).