Recovering the Dash Boots in Eiyuden Chronicle: Hundred Heroes is not possible once they are discarded. Here’s a detailed explanation of the situation:

1. Location and Acquisition:
– The Dash Boots are found in the Abandoned Mine, which you access after Nowa is made acting captain and you’ve acquired at least three allies in Grum county.
– Specifically, they are located in the west-most chest of the third and final section of the dungeon, shortly before the boss fight against the three bandits.

2. Equipping and Usage:
– Once you find the Dash Boots, you can equip them to any party member in the accessory slot, which significantly enhances your running speed.
– Notably, Nowa doesn’t need to be the one wearing them; any party member can use them as long as they are equipped.

3. Losing the Dash Boots:
– If you accidentally discard the Dash Boots, there is no way to retrieve them. They are a one-time item and cannot be bought back or replaced.

4. Alternatives:
– If you need an alternative to enhance movement speed, you can use the Rune of Quick Movement. However, the Dash Boots are more convenient for their specific slot and effect.

Given this information, if you have lost the Dash Boots, you will need to continue with your game without them. If you are significantly far through and losing them impacts your progress, restarting your save might be considered, but it is not necessary unless you are really far along in the game.