You need to have something that keeps changing. Interest will be replaced by boredom if it is the exact same game over and over. But it doesn't have to be.
Many classic games are the same game, but you play them with different people. Chess or Go, for example, have zero randomness except for the people playing. That makes it interesting to keep playing the game.
Other games have elements of randomness that keep the game fresh. Card games or dice games. That means games never exactly repeat and while if you play long enough you will spot patterns, you never actually play the exact same game twice.
A third category is ongoing storytelling. If your game develops over time, even if the core game mechanics stay the same, it can provide interest. Real world wars (seen as games following James P. Carse definition) are not interesting because weapons change, but because they are part of the history of the world. Many roleplaying games fall into this category. The content can be created by players.
A fourth group is procedural content generation. You can make the game endless not just in time, but also in content. If there is always one more world to discover, one more level to explore. This is similar to randomness above.
What I found the strongest factor is human interaction. If you have a multiplayer game, the fact that players constantly adapt to each other, providing a constantly changing environment, you can draw people in a lot. My most successful game, which has been running without interruption for almost 20 years now, mixes the history and interaction elements and is still interesting to players (some of whom have been playing for more than a decade).
In your tapping game, obviously the aspects requiring other people are out. I assume that you already have some randomness, but this aspect is not strong enough to provide gameplay in itself the way that it does in card games (where playing good with the hand you were dealt is often exactly the challenge).
I would advise to play with randomness and procedural content. You can make levels more chaotic as the game progresses so that the skill a player requires slowly changes from prediction to reaction.
By nature, your game is probably most close to a card game. In this class, the successful games all have a very good balance between skill and randomness. While you get a random hand, the game is balanced so that a good player can win with almost any hand, while a bad player can absolutely lose with even the best hand. There are often also multiple ways to win so you can choose a different strategy based on your hand.
Your game may simply be too simple to have these elements that a game requires to be eternally interesting. You may have to add such elements.