Recommendation for HEPA Vacuum For Litter/Fur Problem? Something That Won't Clog Every Other Day

Hi! We've got two Siamese short-hair cats who use and have tried a variety of clumping litter brands on advice of vets and the San Francisco SPCA. The litter is great EXCEPT that our highly-recommended, very expensive SEBO Felix Pet HEPA Vacuum Cleaner with a bag is always becoming clogged. We spend so much money taking it in to be professionally cleaned. We called the manufacturer (USA affiliate) and their tech person walked us through how to take the vacuum apart and clean it and put it back together. The problem is that the vacuum gets clogged way down deep where we can't reach. The vacuum cleaner dealer/ repair guy here in town seems to know a secret. After investing so much money in such a useless machine we're looking for another vacuum. We have wood floors throughout except for tile in two small bathrooms. We really don't vacuum the upholstery much because our cats are Senior and Geriatric and hang out in our bed or in their heated beds with washable covers. The big problem seems to be getting a vacuum that can handle the average amount of fur on the floor, dust bunnies AND the clumping litter bits and the usual litter dust that gets kicked out of the two litter boxes. Has anyone had similar experiences and/or recommendations or warnings about various vacuum brands and models? Thanks in advance for any responses!  

I have a Dyson Animal and I'll never go back to a regular vacuum again!

Just like all vacuums, it will clog is you suck up things that are too big.  However, it won't lose suction from cat dander dust, kitty litter dust or drywall dust.