It is not just Eley.  I've experienced that with a BSA Martini International (last November) and in an original flat spring High Wall in .22 LR just 3 weeks ago.  Extreme hot weather is not necessarily a factor.  Both my experiences were in very mild but damp conditions at the Redwood Gun Club range, Manila, CA. 

Symptoms were failure to eject, followed by failure to extract, and progressively more difficult to chamber a cartridge.

The Martini International gummed up with German-made Wolf Match Extra.  The High Wall gummed up with Aguila Match, the black box stuff.

The mantra with olde tyme smallbore shooters is "thou shall not clean", but the chambers and actions do get gummed up.  An occasional cleaning is necessary

I have never had a problem with Eley Tenex gumming up my three BSA MkII Internationals with a BSA barrel or the ones converted to RKS barrels

I only clean them once a year down to pristine white metal with lead removal solvents and use JB bore paste to eliminate carbon buildups.

They need to have at least a box of ammo through them after cleaning before their best accuracy is restored.

I also only clean the action once a year but lubricate it well with moly lube which insures continual hard extraction of the cases.

Ralph McDonald use to wipe fresh Alberta Schuetzen Lube on his old lube hardened rimfire ammo.

He kept doing it for many years so it must of been beneficial to do so.

I never had any problem with hard lube on the Tenex ammo left over from the 1976 Montreal Olympics.
But one out of ten cases split from being stored in an unheated garage.