DarkGhost

Switching from grid to battery is a signal from control to Relay ... If we assume the relay is working fine, then we check load.
you said Load is 500 to 1 Kw .. that shouldn't make that problem for a 10KW inverter ..
so I advise:
- check grid status (Voltage, Frequency) if the grid voltage is lower than normal that could cause that delay (solution is a good regulator)
- check Cables, if cables diameter is not well calculated or the length between inverter and load is big, that will cause drop voltage which get us back to first case.
- check inverter settings, especially the response time (usually there are two options, one for appliance (20ms) and one for sensitive devices like PCs (lower than 10ms)
- check battery condition, and concentrate on terminal connections, also check connections on circuit breakers if there is any.
- If your system is NOT a common Neutral (combined grid Neutral with inverter output Neutral) that could cause such a problem (thou I don't recommend that kind of install)
 
I advise you to use a small UPS for sensitive devices (routers, PCs .. etc.)
Actually, I've done this with my own system because I have the same problem you have, SPECIFICLY when gaming on my PC
 
hope that help ...

Do you know what the load is when this happens?

Possibly one of the most comprehensive tests was done by Sandia National Labs:
https://iopscience.iop.org/article/10.1149/1945-7111/abae37/pdf

The bottom chart shows the total kWh discharged from the battery from new until it degraded to 80% of its initial capacity.
There is roughly 20% improvement between 100% and 20% DoD.  The difference between 60% and 20% is negligible. Would have been nice to have more data points to find where the knee point is, but it is certainly not much to be gained going much below 60% DoD.
 
What is striking though, is how much difference other factors (temperature and C rating) make.  If you really want the most from the cells, then:
1) keep them cool, and
2) stick at or below 1C discharge.

In general it is not a good idea to only charge to 80%, especially if using LFP lithium. The battery needs to go to 100% to reset the SOC algorithm and (in some instances) balance all the cells properly.