It is really important that you get the setup of the express correct.
Do you have the Express set to bridge mode.. that is a must. (You can try a bridged TG797N and use PPPoE on the Express but it is rather less than likely to work well).
On Yosemite I strongly suggest a bunch of setup details..
Use ethernet to the AEx if possible to make sure your issue is purely wireless side... and ensure you have ipv6 set correctly as per point 5.
The best way to test is full factory reset.
Factory reset universal
Power off the AEx.. ie pull the power cord or power off at the wall.. wait 10sec.. hold in the reset button.. be gentle.. power on again still holding in reset.. and keep holding it in for another 10sec. You may need some help as it is hard to both hold in reset and apply power. It will show success by rapidly blinking the front led. Release the reset.. and wait a couple of min for the AEx to reset and come back with factory settings. If the front LED doesn’t blink rapidly you missed it and simply try again. The reset is fairly fragile in these.. press it so you feel it just click and no more.. I have seen people bend the lever or even break it. I use a toothpick as tool.
Then redo the setup from the computer with Yosemite.
1. Use very short names.. NOT APPLE RECOMMENDED names. No spaces and pure alphanumerics.
eg AEgen5 for basestation and use AE24ghz and AE5ghz with fixed channels for wireless, as this also seems to help stop the nonsense.
2. Use all passwords that also comply but can be a bit longer. ie 8-20 characters mixed case and numbers.. no non-alphanumerics.
3. Ensure the AEx always takes the same IP address.. This is a bit tricky in the TG797n, so skip this one for now. If it is still an issue post again for details.
4. Check your share name on the computer is not changing.. make sure it also complies with the above.. short no spaces and pure alphanumeric..
5. Make sure IPv6 is set to link-local only in the computer. For example wireless open the network preferences, wireless and advanced / TCP/IP.. and fix the IPv6. to link-local only.
6. Test speed in the local network.. ie copy a file too and from a computer plugged into the LAN port of the AEx by ethernet to another device running on wireless, if this is ok, then your problem is purely the AEx itself not handling WAN..
There is a lot more jiggery pokery you can try but the above is a good start.. if you find it still unreliable.. don't be surprised.
Post some screenshots of your setup.. it helps loads.