I must say that I use the Alerts system extensively, particularly to follow military flights. As I tend to be sitting in front of the screen most of the time too, I've never seen the Alerts to fail. The way I use alerts is with plenty of wildcard entries, I don't tend to use the "range from overhead function, but I do use all the others - SSR, Mode S, Registration, Flight ID.
I have the Network traffic turned on most of the time, but not always - and this makes no difference to the alerts.
I'm not sure that I understand what the problem is here, but it's almost certain to be something simple.
Are you hitting the return key after the last entry? I don't do this, I just come out of the entry box after putting in the details.