If you search the Travel Products forum here you will find lots of stories about people getting their Rimowa bags fixed even though the warranty period had already expired. Rimowa is generally known to be fairly generous with their warranty coverage.

So you should do your best to save the paperwork and receipts and keep track of them. But in the end, you probably won't run into a situation where your warranty issue is denied because there is no stamp or date in there.

I recently brought a damaged bag to an independent luggage store that was a Rimowa-authorized service center. The people there just asked me if it was under warranty and took my word for it when I said it was. I had the receipt in my gmail and it was bought 4 years and 10 months before the repair, but nobody wanted to see it. Of course YMMV.