Once you have stained cells, it is necessary to know how long the cells with the fluorochrome on them will remain as you want them.
Cells die with time, antibodies are internalized gradually at warm temperatures, fluorochromes become bleached in the light, and microbes will grow everywhere eventually.
The answer to all of these problems is to keep cells (before and after staining) scrupulously at 4°C and in the dark, use a metabolic poison like azide in all buffers if you are not concerned with recovering cell function, and, finally, fix the cells with formaldehyde after staining if you are not going to analyze them within several hours on the flow cytometer.
Although 1% formaldehyde fixation does change the FSC and SSC of some cells and may increase their background fluorescence and decrease their staining fluorescence just a bit, it provides great cell stability after staining and also a large margin of safety when dealing with potentially pathogenic samples.
A good, general procedure for antibody-stained cells is to fix them in an equal volume of 2% formaldehyde after staining, let them sit at least 24 hours, (covered, in the cold and dark) to reach final FSC, SSC, and fluorescence levels, and then read them on the flow cytometer within 2 weeks (although most cells will last much longer).
Check out your own cells with your own stains before deciding on the length of time that you are willing to risk this. But fixation after staining is definitely the way to go if possible --- giving great flexibility in planning time on that cytometer. As a reminder, you cannot fix cells before flow if you want to use a membrane-impermeant stain like propidium iodide to check cells for viability or to gate out dead cells in flow analysis. All cells become dead and take up the dye after formaldehyde fixation.