First of all, it's NOT YOUR fault, so don't beat yourself up about it. All babies are different and what worked for me obviously won't work for all of mothers.
I also am a SAHM, with a 3 1/2 year old boy and a 24 month old girl. Until recetently they were both taking AM and PM naps. I know if I've fed my children well and played with them a bunch they NEED to nap/sleep. They wake up about 7:30 and go to bed somewhere between 7:30pm and 9:00pm at the latest. But I am as stubborn as they are... We have a routine. They wake up around 7/7:3. During the day I give them a good breakfast, play with them, but I make sure that I put them down to nap between 11:30 and 1:30, unless we're running around. It was 10/10:30am and 3/3:30 when in was 2 naps. If they cry... I let them, for at least a few minutes, not more than 10 minutes. I know that sounds terrible, but you've got to at least try it. Babies konw you love them, but also know when they want something they cry, not necessarily because they NEED something. Both my children took 2 naps until they were about 18 months old. I know with my babies, at this age, it's more of a power struggle. Even at a younger age, they really just wanted me when they wanted me, and it's hard to not give in, but it's not good for either of you. As quickly as they get into the habbit of getting you when they want you, they can get figure out that your not going to run to them at 2, 3, and 4am.
Obiously if your baby sounds like he's in distress I would go to them right away. I know when my babies NEED me, and when they are just over tired or trying to be the boss. Don't be a hard a**, but realize the difference. I have two of the most loving babies in the world. I really do. They are both sweet and compassionate. But I didn't jump every time they cried. I did wait. My son still takes an 1 1/2 to 2 hour nap and so does my daughter. It was longer before they started sharing a rooom.
Sometimes my daughter wakes up in the middle of the night and crys for like a minute, and just goes back to sleep. I don't know, but if you feel in your heart that it might be something seroious you need to ask your pediatritian. That's #1. I hope this helps. Get some sleep.