If you assume coin tosses are independent, it shouldn’t matter if you miss coin tosses.
A person tosses a coin, so tosses are are connected to each other.
Ask yourself this question- Would your thumb hurt if you toss a coin 5000 times? If so, would that change the results?
https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_co...
The paper does discuss coins allowed to land on a hard surface; it is clear that this will affect the randomness, but not clear if it increases or decreases randomness, and suggests further research is needed.
The machine they use to toss the coin has a spring, and Im sure the spring tension varies through time effecting results.