Council Tax Exemptions

Council Tax on a property is payable again 6 months after probate is granted. What would be valid reasons to ask for further exemption?
The property in question is in a poor state (although the deceased lived there with no problems) with an EPC rating of F, so it could not be let. Is this a valid reason or not?
The executors have recently had the property re-rated and it came out at a D given the addition of a full central heating replacement. Does the clock starting ticking again from the date of the new EPC?
Seems that the only thing not affected by covid delaying things is the timescales for paying council tax & the exemptions - that’s a surprise from a monopoly !
There were huge delays in getting the house ready for sale as the Executors could not travel to the property due to covid, and potential buyers were reluctant at the start of the process, contractors to sort out problems were not available etc - all valid reasons in my opinion for the 6 month rule to be extended to say 12 months !
Many thanks.

I imagine it would depend on the council, I know a couple don’t offer the 6 month exemption anymore, but if the property cannot be legally lived in then there is a possible exemption and if it’s derelict then it can be removed from the valuation register all together.

Other councils offer discounts for unfurnished properties or those needing major repairs.

It would be worth applying to the council but as with so many other things it seems to be a postcode lottery as to what is available.