What exactly do you mean by "storage" here? If you're asking if there is way to keep the luminol producing light for long periods of time, no. Once that reaction begins there is a time limit to how long it will last.

However, if you seal the membrane in plastic to keep it from drying out, you can re-probe it later with a different antibody. To do this our lab will remove the membrane from the plastic, wash it 4 times in TBST, block it overnight in milk buffer at 4C, and then apply a new primary that was not raised in the same animal as the first primary antibody we probed with (for example, if the first probe was raised in mouse, the primary used for the second probe might be raised in rabbit). If it does dry out, you can still re-activate it in methanol and then re-probe it. However, this trick does not work with membranes that are too old, even if they have been sealed.

The other option is to use fluorescent probes. While a fluorescent Western blot won't last indefinitely, you can still image the membrane several days or sometimes a couple of weeks after running your blot, provided you keep the membrane in dark location and protected from light. Fluorescent Westerns also have the benefit that you can use multiple primary antibodies simultaneously, however the sensitivity isn't as good as a traditional Western.