There is no reason for it to happen and plenty of reason for it to not happen.
There is clearly a reason for it to happen. It seems obvious to me that it's much healthier to have a money supply which remains stable, then to have a money supply which decreases into infinity; that's like the opposite absurdity of infinite inflation, both extremes are moronic in the long term. From a mathematical, practical, and economic perspective, the most desirable option is obvious. Now please enlighten me with the reasons why it shouldn't happen, other than you want your BTC to go up in value due to a decrease in the money supply.
One I don't accept that the money supply needs to be fixed exactly. The loss rate over time will slow to a trickle and the money supply decreasing by 0.5% a year or (or even increasing by 0.5% a year) isn't a material problem. For all practical purposes the supply is fixed and price is based on demand (which over the next 100 years or so changes in demand will dwarf any valuation changes due to slowly shrinking supply). However lets pretend the money supply "should be fixed".
There are three major issues.
First. Your solution won't make the money supply stable. Valuation is based on the available money supply. If anything your proposal will cause rapid fluctations in supply, and mining rates (to potentially cash in on a once in a lifetime windfall in mining profits). Lets (pulling numbers out of my ass) that in the first 4 years roughly 2 million BTC were lost. We would expect over time this rate of loss to decline as the obvious value of BTC becomes apparent as well as improved technology and best practices (deterministic wallets, auto backups, hardware wallets, etc). So the "lost coins" are to a certain extent already price in. Currently the price is based on effective supply Nobody needs to know how many are lost the market effect of supply and demand will set the price based on effective money supply. As the annualized loss rates continues to decline (in nominal BTC terms) the effect on overall valuations will be small. The difference between an asset whose supply is truly and perfectly fixed vs shrinking at say 1% is immaterial. The change is price will be driven mostly by changes in demand. As an example say 10 years from now loss rate is <1% per year and demand is growing at 35% per year. 35% vs 36% does it really matter? The price is for all intents and purposes determined by increased demand.
However whatever "expiration date" is used means that in roughly x years there will be a massive INCREASE in the effective supply when that window hits. Say 2M coins were lost in the first 4 years. That means in 50-54 years the coin supply (which has had slowing inflation for decades now) will supply see a minting explosion of 2M BTC (which could be worth billions of USD or more). The fear and uncertainty on the true supply would have the exact opposite effect as intended. As we approached the expiration date a lot of volatility would occur as people try to estimate how much new supply is going to crash into the market. Another issue is the risk of overmining. Mining will reach an equilibrium with transaction fees and in 50 or so years should be relatively stable however the expiration of these early 2M coins (which could be worth a small fortune) would cause a massive mining surge. The network will built out massively as the ROI when including this once in a lifetime bonanza of confiscated coins would warrant expeditures than "normal" mining wouldn't. What happens if the hashrate jumps 200x and then 99.5% shutoff after that free money window is gone? Oops. Network needs 400 weeks to reset and until that happens block times are ~1 day each?
Second. It is unfair. There is a social contract in Bitcoin. Bitcoin is voluntary. Nobody is forced to use it and the rules are well known. However what you propose is an "Ex post facto" change. It is material unfair. People entered in Bitcoin because on certain proclaimed truths one of which being that (for better or worse) transactions are irreversible. This is a form of reversibility. You are proposing to change the social contract after the fact and that is ALWAYS unfair. A system built from day one with this change (and other hard fork changes) would be different but to impose it upon people after the fact isn't just unfair it is immoral.
Third.
This is all academic. It simply is NEVER EVER going to happen. Just like the hundred or so last threads nothing is different. Making this kind of hard fork is simply "defacto" no possible (although technically possible) due to the consensus rules built into Bitcoin. Unless a change requiring a hard fork has overwhelming support the other "normal bitcoin" fork will live on. So either one fork will die off or they would compete directly with each other causing chaos and uncertainty which devalues both forks. "Can the real Bitcoin please stand up?"