As one such brand new Americano fan and a relative outsider, let me give my perspective.
First of all, the new fans worth their salt won't be running for the hills after 4 bad weeks. Please. Perhaps we'll lose a few who came for Landon and haven't followed since, but the real fans, the ones who are here for Everton not any single player, they'll stay. Once a team is "yours" it remains so forever. In the face of adversity, some will deal by lamenting their fate, some will deal by distancing themselves from an already distant league, and some will choose a "best of the rest" second favorite team and draw some pathetic echo of joy from their victories instead. But none will lose their love of Everton; we aren't so flighty as all that.
Secondly, some random disconnected thoughts about happiness and sports.
There are multiple kinds of happiness, as well all know. General contentment, pride in an accomplishment, a fun time with friends, etc etc. Sports happiness is a very specific kind, and it does not come in a simple one-to-one ratio with victories. Otherwise we'd all be fans of the same team, which would never lose. No, in sports we define happiness as something more - epicness might be the better word; passion is also closely related.
So yes, there is a certain joy to be drawn from gloryhunting. But that is not what we were seeking, originally, when we each became fans of this team, this sport. We sought that certain brand of happiness that comes not in spite of, but because of the obstacles - the kind that demands sacrifice before it will show itself.
It is easy to declare your allegiance for a team you care nothing about - any team, any sport - and derive some peripheral pride or temporary joy from a victory you didn't even watch. What is hard is to love a team, and to stick with that team through terrible times on the promise of a reward which may never come, but which, if achieved, would be worth all your effort by a factor of a million. This is what sports fandom is about; the constant barrage of stress and disappointment in return for those rare shining moments. When, if ever, Everton wins something big or my Sharks lift the Cup, everything will be instantly worth it.
I have two friends who are Chelsea fans. One is a gloryhunter who chose the team last year. The other is a lifelong fan born into it because of family ties. The former watches only highlights and tells me constantly how "awesome" Chelsea is doing. The latter is simply basking in what he calls the "glory days." I'm jealous of the second one, having never experience glory days for any of my teams. But the first one, not at all. I'll take Everton love and failure over vague Chelsea interest and success any day of the week.
My point is this: Don't start talking about cutting your losses and avoiding this misery. We watch sports for the indescribable feeling of an epic moment, but we also watch for this feeling: the frustration, the disappointment. It's about passion, one way or another.
So am I annoyed that I've been getting up early on Saturday mornings and losing precious sleep to watch crappy soccer? Yes
Am I regretting that Everton chose me and contemplating a swap to the other Blues? Hell no.
Besides people, geez, it's only been 5 games, one of which was actually pretty cool. Chill out!
(Please forgive this verbiose rant; I was kind of in a mood...)