  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, $P_\mathrm{d} = 278.36$ 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 $P_\mathrm{d}= 278.36$
d, but the observations show no transit. We find that large ($>22.4$ hours)
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 $P_\mathrm{d} \neq 278.36$ 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.
