If you are unable to pick up daily pledges, first make sure that you have completed the quests "One of the Undaunted" followed by "Taking the Undaunted Pledge." If this has already been completed, please make sure there are no leftover pledges from previous days.

Can you do undaunted pledges on every character?

The Undaunted Pledges are repeatable quests which become available at Level 45 from the Undaunted Enclave in your Alliance Capital, and task your group with clearing out a dungeon. It is possible to complete up to three pledges per character per day and each type of Pledge can be performed every 20 hours.

Can you solo undaunted pledges?

There are achievements you can get that will give you xp towards undaunted skill line, but not enough to avoid doing pledges. There are probably a few pledges you could solo, depending on the dungeon and how you like to play, but generally speaking it's much faster to do them as a group.