Have you even spent an hour or two looking at U.S. Census records trying to find someone who obviously lived during the census year, but for some reason refuses to appear? Usually, the problem either lies with the index or transcription of the name by the enumerator. In either case, the person or even whole families can be rendered invisible. Sometimes you begin to suspect that the person avoided the enumerator for some reason or another. If you happen to find the person in either a U.S. Census before the one you are searching or after, try looking page by page through the place they lived in the Census in which they were found. It is possible also that the person was in transit, moving when the Census was taken.
However, if the problem is with a particular index to the U.S. Census perhaps you need to look for the same census year in another online source or two or three or four or whatever. For links to a variety of sources for different copies of the U.S. Census online see United States Census in the FamilySearch Research Wiki.
Hmm, and how about State Censuses? Maybe the state where the person lived did an interim census? Many states conducted censuses in between the U.S. Census. For an example of what might be available and for an extensive listing of all of the resources for search U.S. censuses, see the FamilySearch Research Wiki article Utah Census. Look in the Research Wiki for each state or country for similar articles.
If your ancestor lived in a sizable city, you might want to try searching a City Directory for the same time or place? Hmm. I realize when you are determined to crack the code of the census, it is difficult to switch gears and go to an entirely different type of record and unfortunately, City Directories are not nearly as well represented online as the U.S. Census and they may take some searching in state and local libraries. I found an extensive collection of City Directories in the Utah State Archives and another collection in the Church History Museum in Salt Lake City, Utah for Utah cities. You may have luck finding them in local libraries or even in the State Archives or Libraries for the area where your ancestor lived.
What, you say, actually go somewhere to search for records? How Twentieth Century! Yes, I suppose, since genealogist dwell in the past that we are still retro and searching paper records. But until I find local records being digitized wholesale online, I will still get in my car and drive to the libraries and other repositories. Ancestry.com, FamilySearch.org (in the Family History Library Catalog), and other online websites have a smattering of directories, but ultimately you have to go to a place that collected them.
When you get mired down in one type of record, you begin to lose perspective of what other sources may show the same or similar information. In addition, the fact that a person did not appear where expected in the U.S. Census is not "proof" of anything. If you have found the person in other U.S. Census records, it is possible that your particular person was missed. The question at this point is whether or not finding the additional record adds to the total information about the individual or family that cannot be found in other records?
Obviously, this topic is highly open ended. I am currently writing a series of articles for the FamilySearch Research Wiki entitled generally, "How to Find..." Ultimately, I hope to have someone else pick up on the project, but right now I am starting with a page called How to Find Genealogy Records, with links to other articles on the subject for each type of record in the Research Wiki. I will also be filling in the gaps if there are now current pages on the subjects. There are also many articles on the same subject about countries other than the United States. You will see the list when you search for "How to Find." Today, when I did this search, I got over 13,000 articles.