I'll broadly define failure as not having achieved initial goal.
That said...not making a profit is not necessarily failing. Facebook, for a long time wasn't making a single cent...I think LinkedIn as well. But they're achieving their goals. And so haven't failed.
I wouldn't know if these guys are profitable (inside nfo)...but in terms of CONSISTENTLY getting the eyeballs and achieving their primary goal, I believe are succeeding:
Techzim (www.techzim.co.zw)
Zimbo Jam (www.zimbojam.co.zw)
EatOut (www.eatout.co.zw)
New Zimbabwe (www.newzimbabwe.com
Classifieds (www.classifieds.co.zw, a WebDev product. Webdev isn't necessarily a startup but the Classifieds project could be considered one)
These are just web based startups....I'm sure they are a few more that are tech but not necessarily web based. If we open the field up to all start-ups in general, not just tech..then there could be a few more.
But this then also proves my point that start-up activity in Zimbabwe is low.