Don't get too hung up on this problem - it will very likely go unnoticed by your audience. I really wouldn't recommend using an electonic tuner for practice, because singers (usually unconsciously) don't use a tempered scale - the intervals a good singer uses are ever-so-slightly out of synch with those of a fixed-pitch instrument or tuner. That's one reason that unaccompanied singing can sound so magical.

I can usually maintain pitch pretty well, although I sometimes end up slightly sharp, possibly because I'm over-compensating against going flat, which always sounds worse. I find it helps to think of pushing the note up from underneath it and suporting its pitch from below, or (alternatively) to think of hitting the very top edge of the note.

It also helps to get your breathing sorted so that you're not running out of breath at the end of lines, and to stretch your mouth cavity into a sort of internal smile when you're going for an upward interval.

Some lesssons could help, or just practice alone doing things like semitone scales, or trying a song with big intervals and testing at stages to see whether and when you've lost pitch.