Ebbsfleet failed to overcome Stockport despite the visitors playing with 10 men for more than an hour.
Jon Nolan forced a fine save from home goalkeeper Preston Edwards early on, but County then had Alex Kenyon sent off for elbowing Neil Barrett.
The hosts laid siege to the Stockport goal, but Richard O'Donnell saved from Liam Enver-Marum and later tipped over Josh Scott's close-range header.
Fleet continued to push for a winner late on but Tom Phipp fired wide.
VIEWS FROM THE DRESSING ROOM
Ebbsfleet manager Liam Daish told BBC Radio Kent:
"It's a stat that could haunt us - we've drawn too many games at home.
"We had opportunities to take all three points, we don't take them and we get anxious. That's been the story of our season.
"Today we haven't conceded, but missing chances is costly for us."