A lot depends on what the material is.
For steels, for example, I have seen a concern by users with products being produced with "old steel". There is an impression that products made with "old steel" are considerably inferior compared to those made with "new steel". In fact, I have seen product specifications that require the parts be manufactured by steel that has been received by the manufacturing facility within the past 3 months.
On one hand, this is ridiculous. As racookpe1978 has stated, the steel isn't going to change by sitting on the shelf.
From a practical standpoint, however, I can see know why this perception exists. If a shop has a piece of steel stock that has been sitting around for 10 years, you can bet there is a reason it hasn't been used. In that time, the people who knew the reason not to use it (and, therefor, would know what types of products it could be used for) have moved on (retired, found a better job, were promoted, fired, or laid-off). But, the stock is still on the shelf with the heat number steel stamped. Ten years later, someone finds the steel, runs the MTR from records and finds that it seems to be fine. They use it and the product fails, because the steel had serious quality issues not reflected on the MTR (heavy stingers, internal bursts, spotty hardness, there could be a host of issues why the quality was bad).
Another issue with old steel is that in the time it has been on the shelf, the identification could be lost. Someone saws the stamped end off to use for a part and mis-stamps the traceability number. Next inventory, it is found to not have a valid traceability number, so they make the assumption that it should be the same as the piece next to it. Traceability is lost, but it appears that the traceability is good.
While both of these could happen with new stock, it is much more likely to occur the longer the material stays around. Most places I've worked had a policy that any material over 3 years old had to be signed off by the plant metallurgist and I've scrapped material just for being old and I wasn't sure I could trust it.