Foam is gone after fridging, Should not I fridge?

I am with barking.pete and chthon on this but would go even further in assuming that something with the carbonation process itself is off. In my (for obvious reasons limited) experience of opening warm beer bottles, there should be much more than just foam and some carbonation if you open a well carbonated homebrew at room temperature. So I assume that the CO2 content of your beer is already too low before it goes into the fridge. As barking.pete and chthon have both pointed out, lower temperatures mean much higher CO2 in solution, if you look at the numbers for a fairly standard carbonation of 4.5g/l, the overpressure in the bottle is 1.74bar at 20°C, whereas after a period of time at 7°C this goes down to only 0.8bar. If you are unsure about the carbonation of your beers, I suggest you invest in a bottle pressure gauge. I use one on any beer I bottle carbonate to check carbonation progress and as an early warning system against bottle bombs. To entertain my curiosity, how much sugar do you add to your bottles and what temperature do you ferment your beer at prior to bottling?

//late edit: Another source of issues could be the amount of headspace. If there is too little space above the beer, not enough CO2 volume is present to be dissolved into the beer at lower temperatures.

I doubt this is a case of "stale beer" - I suppose it is just not very carbonated for service at a cold temperature.

The metal cap of a beer bottle tends to shrink faster than the glass so the cap becomes more firmly attached as the temp drops. It is possible that the cap is badly fitted and that may affect gas tightness, but this is rare. Crown corks are used because they tend to work. ! or 2 failures maybe, but the lot?

More probable is the fact that CO2 dissolves more in cold liquids and so the head pressure and the foam may reduce in cold beer. Also the gas stays in solution in cold beer when poured. On the plus side the beer usually remains "fizzy" to the taste for longer. If you want more foam add a foaming addition (dextrine malt or even malto-dextrine for example) to the brew and/or add slightly more priming sugar when bottling.

If your beer really is stale, that would mean that you have a problem with the caps on your bottles because of the low temperature, and that somehow your CO2 escapes and oxygen enters.

However, at lower temperatures, more CO2 dissolves in your beer. If you keep your beer really at 4° C, that is very low. My experience is that keeping a beer for a couple of days at a low temperature does not give a good head, because not much CO2 is available. However, putting it a couple of hours at a temperature of 8-12° C improves this.