This is just from what I've seen personally.
- Denied because person wasn't Orthodox
- Denied because the person was a practicing homosexual
- Denied because someone convinced another to get an abortion
- Denied because a person kept committing the same sin over and over (to hopefully teach them the seriousness of the situation. Denying someone for this reason can help them wake up and not take communion for granted)
- Denied for not being dressed properly (low cut top on women, shorts, stuff like that)
- My priest told me in Russian some people get denied for not wearing their cross
- Denied for not fasting before hand (without otherwise been given a blessing to do so, for an illness)