As always, the situation is more complex than it first appears. The OP has provided some information and we're figuring out the probable reason.
Fixed deposits are acceptable as POF without doubt. But the same logic applies to them as to any other account being used to showcase POF. It is the PA's responsibility to prove beyond doubt that the funds being showcased for POF purposes are not borrowed. Whether the funds are in the form of checking/saving account or fixed deposits, this requirement stays unchanged. If the funds have been around for less than 6 months, the applicant has to conclusively identify the source of funds for CIC's benefit and prove that the fund weren't borrowed. If the funds have been around for more than 6 months, it shouldn't be a problem usually but an officer might ask for source of funds if they suspect something.