HIP 41378 d is a long-period planet that has only been observed to transit twice, three years apart, with K2. According to stability considerations and a partial detection of the Rossiter–McLaughlin effect, P_d = 278.36 d has been determined to be the most likely orbital period. We targeted HIP 41378 d with CHEOPS at the predicted transit timing based on P_d = 278.36 d, but the observations show no transit. We find that large (> 22.4 h) transit timing variations (TTVs) could explain this non-detection during the CHEOPS observation window. We also investigated the possibility of an incorrect orbital solution, which would have major implications for our knowledge of this system. If P_d ≠ 278.36 d, the periods that minimize the eccentricity would be 101.22 d and 371.14 d. The shortest orbital period will be tested by TESS, which will observe HIP 41378 in Sector 88 starting in January 2025. Our study shows the importance of a mission like CHEOPS, which today is the only mission able to make long observations (i.e., from space) to track the ephemeris of long-period planets possibly affected by large TTVs.