It sounds like this new policy is in direct response to employees inability to clean up after themselves without management intervention. Even if you personally take care to remove your items from the kitchen space in a timely manner, if the majority of your coworkers were not doing this, then management was probably spending an undue portion of their "billable" work hours handling complaints or possibly even cleaning the space themselves. Since it is a work environment, enforcing a policy that seems unfairly strict is an acceptable solution since it reduces wasted management time, and therefore cost.
There are a few ways you can handle this.
1) Get used to it. I'm not saying this to be unhelpful - I'm suggesting giving this policy a fair trial, trying to see advantages and disadvantages. There was a policy like this at the first company I worked for, but because it was always this way as far as I had experienced, it didn't seem unfair - in fact, it was really very nice that our workplace kitchen was never cluttered or stinky. Nobody ever had a problem finding space to put their lunch in the fridge, and because there was never any "mystery" food that nobody remembered who it belonged to, instances of coworkers eating each other's food were very low. You may not find that these benefits occur in your situation, or they may not seem equal to the hassle for you. But by giving the policy a chance and logging your findings (good and bad), you will at least have a comprehensive case to present to management if you ask them to reconsider the policy.
2) Remove the need for the policy. Can the dirty kitchen problems be solved another way? If your office is small, you can place a bin for each coworker with their name on it, and ask management to try discarding only "unclaimed" items. This introduces personal accountability in the kitchen space; employees may be more conscientious about their rotten food or growing tupperware cache if it can be traced to them. Alternatively, you could require everyone to date their food items, and anything dated more than a week ago will be tossed. The key thing here is to reduce or eliminate work that your managers need to do to maintain the kitchen, because that is what this policy is doing for them.
3) Adapt. Other users have suggested bringing a lunch you can keep at your desk on cleaning day, or using email reminders to make sure you take your items before the purge. You could also try organizing a monthly lunch with your team or just some of your favorite coworkers so you don't have to bring a lunchbox that day. Or make arrangements with a coworker to save each other's stuff if one of you is in a meeting and aren't able to remove your belongings from the kitchen in time.