There are several different ways used to make tests difficult to pass:
Many tests use hybrid approaches--for example, Octec requires both a scarce resource (crystals) and labor (assembling the silver, glass rods, and other materials).
Labor-based tests are the only ones which impose no limit on the number of people who may pass. Unsurprisingly, more people pass labor-based tests than any other kind. Since most tests of Architecture and Worship are labor-based, more people have passed tests in these disciplines than any other.
Resource-based tests are susceptible to use of mules. Even in the abscence of mules, resources from short-term players can create a glut on the market. The degree to which this is a problem is highly variable. Octec is unquestionably easier to pass than it used to be, due to the glut of crystals from mules and quit players. Mentorship is still non-trivial. (Whether the glut of Octec crystals is actually a "problem" is debatable.)
Time-limited tests are the most difficult to tune properly. Pass too many people per time period, and the test will lose its challenge. (When a group can pass Pilgrimage with a single tithe, Pilgrimage has become a trivial test.) Pass not enough people, and the test becomes overwhelmingly difficult.
Perhaps one of the most interesting tests in terms of pass structure is Khefre's Children. The only hard limit on the number of people who can pass is the time it takes to fill and vote on the level-3 beetle garden. If interest wanes in the test, however, the time it takes to fill the garden will increase, bringing down the frequency with which people pass.
There is a problem with most of the time-limited tests. As of this writing, there are 1147 current characters who have passed at least one test of Architecture, 920 who have passed at least one of Worship, 54 who have passed one of Conflict, and 53 who have passed one of Thought. The disparity is obvious.
There are problems which arise from this. The endgame requires players at every level in every discipline--there must be at least one character with seven tests passed, at least one more with six or better, and so on. With very low passage rates, this may be difficult to achieve. (Whether this will be a problem in this telling, I cannot yet predict. However it is clear that there will be very few people who have passed even three tests in Art, Conflict, or Thought.)
Another problem is that achivement is entertaining. The fewer people that pass a test, the fewer people that derive fun from that success. This must, of course, be balanced with the fact that a test which is trivial to pass provides no such feeling of accomplishment. (I suspect I had a far better time passing Pilgrimage back when it was contested than someone would these days by passing with a single tithe.)
One fix is to simply up the passage rate. The problem is that this will be exceptionally difficult to tune properly--the difference between "too low" and "too high" is likely to be razor-thin.
What is needed is a system that adapts itself to the playerbase. Below, I propose one.
First, decide roughly what percentage of people who attempt a competitive test should be able to pass it. I suggest 1/3 as a reasonably good figure--high enough to let a good number of people pass, low enough to retain a feeling of accomplishment.
Define what criteria a player must satisfy to be "part of the test". For judged objects, such as opticons, gardens, and empty hand towers, this would be having a certain number of votes on the artwork or puzzle. For conflict games, this might be playing a certain number of other players.
Define a minimum number of competitors for the test to begin. No player passes unless at least this number have satisfied the enterance requirements.
Once per day, rank all the participents in the test. Each player receives a score--opticon designers get the score of their highest- rated opticon, conflict gamers get their rank as a score. One rule: A player who has passed the test can never have their score drop below their score at the time they passed. (This is important to prevent gaming; see below.)
Take the pool of all players currently participating in the test, not including quit players but including those who have passed the test. Sort them according to their score. The top N% all pass the test, if they have not passed already. (The exact percentage is that determined in the first step above.)
Under this system, the number of players who pass the test is purely a function of the number of players actively competing at it. A player passes if they manage to be in the N% of players on any given day.
A player who initially fails to pass can try again, by redesigning their artwork or attempting to reach a higher conflict rank. Each new person to reach the upper ranks will raise the bar for those who follow. Passed players who leave the game will, in contrast, lower the bar. Both these aspects seem to be features to me.
It might make sense to require that a player remain in the top N% for a certain period of time--perhaps a week. This would act as a counter to gaming, by giving voters time to vote down the score on an artificially-inflated artwork.
The requirements for entry into the test should be moderately restrictive, to prevent Egypt-wide gaming of the system by inflating the pool of competitors with people who have no intention of passing. In the case of art/thought tests, the existing requirement to build a mildly expensive building and accumulate 14 votes is probably more than sufficient.
A test based on this system will never decay to the point where it is trivial to pass, as Pilgrimage has done. The existing players who have passed remain as a part of the competition. (I'm not necessarily recommending that Pilgrimage use this system, incidentally; it's just the best example I have of a time-based test which has become noncompetitive.)
Equally, a test using this system will never become impossibly difficult to pass. A new player simply needs to be better than 2/3 of the current players at the game.