She only has the one thing doing magic damage, but its a spell you pump out once every 2 seconds. Between that and the AS boost you get, you can keep yourself health by throwing in the gunblade. The liandry's torment will give you the %health you need to help bring down tanks (should be built almost always against tank heavy teams). You build the dead mans for the move speed, armor, and health. And you build the Abyssal for MR/AP. If they don't have a big AP threat, you build a lichbane/rabadons instead of the abyssal.
You're not building her tanky so you can tank. You build her a little tanky so you can survive long enough to do eve things without getting obliterated.
Point is, if you're not varying your build with Eve, you're going to get pooped on often. The only time I play pure glass cannon eve is when at least 4/5 of their team is building squishy. In terms of what you can build, there's really very few champions that are as versatile as eve. Building the same thing over and over again especially against team comps that flat out counter eve will not win you games. Hell i've even built her Bork/BC/Cinderhulk/mallet/Maw/Tabi (don't forget her damage abilities scale off AD well too). Also done triforce tank builds on her. You build what you have to in order to win the game. That's how you provide value for your team.
I've played a good amount of eve and trust me, this is what works. You do more damage when you're alive than when you're dead.
Also, try udyr as a champion to play when the enemy team comp looks like it won't work well with eve. Literally anyone can play udyr.