Airplay did run with the A1084 until recently. Even if Airplay no longer runs with the A1084, why doesn't the Airport Base station show in the menu bar, as it did for a time yesterday while I set up the A1084 with Airport Utility 5.6, before it disappeared when the set up was complete? Is there any current use for an A1084? I note that A1084s are being offered on Ebay for as much as $95.
Apple's support document specifies Firmware 7.4.2 is required for AirPlay. Your original Express is capable of running Firmware 6.3, no later, and I still do not know what program you are using for which you require AirPlay.
It's a fine product but AirPlay was introduced long after the A108x was discontinued. As far as I know it should still appear as a device for iTunes music streaming though, unless a recent iTunes or OS X update broke it. I no longer have any original Express models to test.
If its disappearance remains unexplained even after rebooting your Mac and the Express, try reapplying the OS X 10.7.5 Combo update here: http://support.apple.com/kb/dl1582
If you are using any third party "anti-virus" or firewall software, disable it.
I plugged a model A1034 Airport Extreme Base Station into the Verizon DSL Actiontec GT704-WGB modem with an ethernet cable and now the AirPlay icon appears in the Itunes window immediately to the right of the volume control and I can select it and play Airtunes wirelessly through the A1038 Airport Express Base Station in another room connected to a stereo amplifier by a Monster mini-to-RCA left/right audio cable running from the output jack on the A1034 Airport Express Base Station into the CD jacks on the amp. The problem is that I have to select the Apple Network Airport Express Base Station as my network in order to select the Airport Express Base Station when I click the AirPlay icon, which means I have no Internet signal to the Imac. If I select the Airport Extreme Base Station or the Verzion modem as my network, then I have an Internet signal to the Imac, but the Airport Express Base Station is grayed out when I click on the AirPlay icon, so I cannot select the Airport Express Base Station and send tunes to the Airport Express. It would be nice to play Airtunes while simultaneously accessing the Internet. I don't understand your question about what program I am using for which I require AirPlay. I am not learned about computers in general, and even less so about Macs than PCs. I thought the program I was running was Itunes, and there was no separate program to run to use AirPlay for the purpose of sending a signal from the Itunes on the Imac to the A1084 Airport Express base station in a another room, and then out as described above to the stereo amplifier to listen to Itunes music remotely in the other room, without any kind of cable, wire, etc., connecting the Imac to the stereo amplifier. I would guess that the most common use for the A1084 is to play Itunes through a stereo in another room without the need to run wires from the computer to the stereo. I realize it would be easy simply to run a very long mini-to-RCA left/right audio cable across the floor connecting the Imac to the amp without the need to use AirTunes, Airplay or any kind of AirPort, but it would be both unsightly and a tripping hazard.