Actually no.
If your team runs and you die, it's not because your items are bad, it's because your team is bad.
And again no, tanks shouldn't always last through a teamfight. A good tank does one of two things. He either jumps in and locks down his target until his team can assassinate them, or he jump in and he provides such a threat to the enemy team they have no alternative but to blow their CC and damage on him.
If I'm playing Malphite, I fully expect to die each team fight. My style is simple, I flank the opponent, my team fakes an engage, and I ult in. By the time the enemy team is able to react, the carry and one or two other squishy targets are half health or below. They don't have a choice, I'm Malphite, I eat carries for breakfast given the chance. They have to blow ults, CC, every major cool down on me or else lose their carry. I die, but suddenly my team is on top of them cleaning up. The trade ends with 1 for 5 and we get a tower.
Obviously this is an optimal situation, but I've been in it a lot in the past and it's a strategy that I've found works.
I don't count myself weak or my items bad because I died, they did what they were meant to do, they forced the entire enemy team to focus me because they all knew that if one just tried to take me on while the rest went on my team, I'd never die.
If a tank lasts through a team fight, it means that your game is a shut out, that every one of your lanes is fed and the enemy team has no damage. If it's a close match, expect to die, you're a tank, it's your job to bite the bullet for your team.