My dads 98 ford taurus would not stay cranked. It was the idle air control valve. It may be called something different on Hondas. Possibly the idle control solenoid valve or the electronic air control valve (eacv). Mine had or has the same problem on my 91 crx si with the stock motor. I just took it off, sprayed it with wd-40, moved it around, and noticed a difference. It runs better now, but is still messed up. It really needs replacing. I could possibly find it in a junk yard for cheap. These are fairly expensive parts. Not saying this is your problem, but maybe.