my guess is there is something in your tap water that your plant doesn't like, some salt or something I don't know but I had the same problem.
I started growing in an apartment and because I was paranoid about my water and electricity consumption I used CFL's and bought RO (reverse osmosis) water from the grocery store, and I didn't really have any problems, I had bought a digital tds/ppm pen and had all the ph up and down and testers but never needed any of it after the first few weeks cuz everything just worked pretty good.
Then I bought and moved into my own place on an acerage. I had the well water anaylised and it was good, and thought I could save some money by just using tap. At first everything seemed fine. Germinated just fine, poked outta my rockwool cubes fine and lasted about a week or two and had a few leaves out. Then, slowly, one by one they all started looking like that whilting one you got and all started dieing. I lost about 6-8 plants.
I tried everything, got all anal about my ph's, ppm's, airpumps etc. Finally I went back to using the RO water from the store and bam, up and running again, no problems.
where I live its pretty cheap, $10 for a 5gal bottle, $2 to refill and I go through about 5-6 bottles a week. Soon I'm going to buy and install my own RO distilation system but until then I'm more then happy to buy the bottles as long as they keep my ladies looking hot.