Home kitchen hood filters are usually not that good, at least comparing them to commercial hood grease filters (of course, the commercial hood may well cost as much as a used car, or perhaps a new car, and the home hood, not so much.)
If you generate a lot of atomized grease and greasy smoke, some will make it through the filter and be deposited on the components after that point. How often you'll need to clean the hood varies quite a bit with what you cook under it.
You might want to step up the filter washing to every month, or even two weeks, rather than a couple of months. This is entirely cooking dependent so what works for me and what works for you will be different; I clearly fry a lot less than you do, based on your reported required degreasing frequency. But a totally clean, not very effective, filter will still be not very effective, so you might also need to look at cleaning inside the hood more frequently to stay on top of the problem.
The typical aluminum mesh filter in most home hoods is lightweight, inexpensive, and not terribly effective at trapping grease. They are generally claimed to be dishwasher safe, though due to the common interaction between lye in most dishwasher detergents and aluminum, they may discolor. A stainless steel baffle filter is typically more effective, heavier, and more expensive - and may not be available for your hood at all.
In most places the commercial hoods still need to be cleaned every 6 months or so to prevent fires...