Very probably, Beetroot have to be handled very carefully. Dig them without damaging them, do NOT cut off the tops but grip the tops close to the root and wring the tops off. If you cut the tops off or scrape the roots clean you will cause them to bleed and the colour of the root will be lost. Just wash off the dirt and boil the roots, then when boiled they can be peeled and sliced for pickling.
If its only the tops which have gone soft you may still be alright with the roots.
I was given some beetroot (straight out of the ground and with the tops intact). I left them a week before I did anything. I sliced off the tops (they had wilted), but the beet was OK. I cleaned them by using a soft bristled nail brush, and then boiled them for a couple of hours or so and then pickled them - and they are gorgeous.