Hello @coolcastro 

Thank you for your post, if kasa device offline and could not be controlled via kasa app properly, Alexa could not control them either. 

For the kasa device unstable issue, you could try some suggestion here: 
1. Make sure the kasa device is receiving good Wi-Fi signal:
Kasa app-> Device Settings-> tap router Wi-Fi symbol->  signal strength (value of the dBm)
(-40d- 70dBm is good to average, less than -70dBm is relatively poor : relocate smart devices or router closer to each other)
2. Please confirm kasa device firmware and kasa APP version are up-to-date 
3. Ensure smart device is connected to main router directly, not through AP or extenders
4. You could try to change a different 2.4Ghz Wi-Fi channel on router and see if that helps 
5. Turn off Advanced wireless settings like Wi-Fi Optimizing (Channel Optimizing)/ Band steering( Smart Connect )/ Mesh feature etc

If the concern persist, can you help confirm some information to locate the issue: 
1. The Router model:  
Does smart device connect to router directly or through extender nodes in a mesh system? 
2. How about the LED on smart device, the smart plug, when issue occurs, is it red or green? 
The  frequency of the issue:
3. Can you access the kasa device locally (when phone connected to home Wi-Fi) when the issue happens? 

4. MAC address of the kasa device (please share via private message)