How long should a person attend a church that does not have any elders or deacons? What are some of the problems associated with a church not having any elders or deacons?
The follow-on question is: Are there no elders because none one currently attending is qualified, or are there no elders because the congregation refuses to appoint the qualified men present?
If no one currently attending is qualified, then the problem is one of growth. While the qualifications for elders are strict, they are not impossible for many men to eventually reach. Yet in small congregations, it might be difficult to find two or more older men who met the qualifications. What is really needed is for young men to be taught and encouraged to strive and to become elders one day. It takes time for men to mature into the job.
Sadly, in many congregations qualified men don't want the job because it is seen as being too difficult. And they might be right. I've seen a number of groups who make being an elder a life of misery. "Obey those who rule over you, and be submissive, for they watch out for your souls, as those who must give account. Let them do so with joy and not with grief, for that would be unprofitable for you" (Hebrews 13:17). It becomes an endless cycle because those with the wisdom to teach Christians to live in harmony are driven out by disharmony. While it is a bad situation, the proper thing to do is to teach Christians how to be true Christians.
Worse are the congregations where some (it is almost always a subset) refuse to have qualified men to be elders. Often they demand more of the men than what God stated. By putting the entrance bar above anyone's reach, they avoid having to submit to anyone else. And that is probably the key issue in most places. You have people calling themselves Christians who have not learned the lesson of submission (Ephesians 5:21). In some of these congregations, you will find the qualified men working as elders in the background. They are the ones everyone goes to for help with their problems. They might not wear the title but by their actions and deeds, they are the ones watching and care for each person's soul. Such men should be honored for their work because it truly becomes a thankless job.
Congregations without elders and deacons manage to operate, but they do so inefficiently. Decisions get put off and are replaced by endless discussion. Problems aren't noticed quickly, if at all until things get out of hand.
It is clear that God wants elders in His church. But unless a congregation is actually avoiding appointing elders, the lack of elders is not a reason to leave a congregation. Without people encouraging and pushing toward an eldership, it won't happen.