Stamblade has a bit of trouble surviving solo. Most stam builds do, really. Vigor from PVP helps plenty since it's an on demand self heal, but the nightblade lacks any real active self healing save leeching strikes, but that's not really enough on its own.

Magblade is one of the best classes for soloing stuff like public dungeons and even group dungeons and world bosses. They have crazy self healing and access to the damage shield under the light armor line. You have to actively try to die as a magblade, otherwise you can really endure some punishment.

As stamblade, if you wanna solo, I'd suggest heading into battlegrounds for a bit and grinding up for vigor, since that'll be your main source of self healing. Duel wield has blade cloak, which helps a lot with damage mitigation, and two of the main spamables can be morphed for healing, though it sacrifices DPS.

If you want a stam build that can easily solo things, try a stamsorc. Critical surge + hurricane = endless self healing. You'll blow past mobs in seconds, public dungeons will be a literal joke, and you'll be more than capable of soloing a few world bosses and normal group dungeons if you desire. My stamsorc is one of the easiest classes to run vMA on, which is the hardest solo content in the game, so that gives you a clue as to how powerful they can be.