Do you try to max out every time you lift?
Not really, no, I only deliberately max out once a week, usually on Saturday - although sometimes I choose to make Saturday my extra rest day instead. I'll just like pick 2 muscles - say biceps and quads, or chest and upper back, or something, and max out in order to generate benchmarks, that way I can see if I'm plateauing or what.
Sometimes I end up with new maxes during the week but it's not a deliberate "I'm going to max out today". It just comes about as a result of a "push to your personal limit, not a number you wrote on a page" philosophy. It just depends on how I'm lifting and how hard it feels. I suppose that in reality, my maxes increase artificially quickly sometimes if I don't have a spotter one week so my "max" is really only as hard as I can max out while still being safe, whereas the next week I have a spotter so in addition to the gains I may have made since the previous week, there's some portion of additional effort I'm able to put directly into the push rather than the balance and so it gets artificially inflated a bit. I'm sure there's also fluctuations based on sleep, nutrition, etc.
Usually the way I end up generating a new max is simply that on my final set, whether it's 3rd or 4th, I will increase by a larger increment of weight than I did on the 1st-to-2nd set, and sometimes that increment might push me up to a larger weight and I'll do it to burnout.
Today I pushed my 2-hand curl max to 170 simply because I am home for the holidays and even though I did arms yesterday, the cable stack on my regular gym only goes to 150 and I managed to (not so safetly) get it to 165 by putting a 10 and 5 on the plate key. But the gym in my hometown where I went today must have a newer or larger version of the same Icarian machine because it goes up to 200, not 150, so I wanted to take advantage of the opportunity and try 170.
i also got an opportunity to use the ankle weights I used to love (the gym I went to today is actually the gym I went to for about a year and a half before I moved to graduate school so I know it). Anyway I used ankle weights back in the day quite a bit - on leg raises, pullups, box jumps, etc - but my new gym doesn't have them. They have a belt w/ chain but I don't understand how anybody uses that for pullups, it crushes my crotch against the chain and digs into my lower back w/ the edge of the weight belt, it's insanely uncomfortable. Since I used to train as a Marine, I always placed a lot of emphasis on pullup counts and I found that going from doing large numbers of pullups to doing weighted pullups (got up to doing about 6 with 100 lbs or about 15 with 60lbs) generatd quite a bit more size in my lats and shoulders than just doing like half a dozen sets of 20 or 22 unweighted - AND it pushed my unweighted max pullups to around 35, WAY higher than the 20-22 I was able to do back in the MC days.