Not one for keeping seeds for years and do save a lot of my own seeds each year, sowing them within the the next two years.
Mind, it is known that parsnips are known to have a short storage life, so need sowing within its first year or so.
Think also with parsnips, they are probably the slowest of seed to germinate and I think many just become impatient with them rather than failure.
Many methods I have seen over the years on here to try to get them off to a kind of quicker start can help.
Think the general and sensible rule to work with is seed you buy or save yourself generally has a 2-3 year life.
Have with many little experiments over the years found that Spinach, Chard and kale seed lasts for a good five years.
Have also sowed some of my saved tomato seed that is a good four to five years old with success.
Some that fail to germinate recently I have found is my saved and bought gherkin and cucumber seed that is more than two years old, whereas the newer seed germinated fine, growing in the same tray.