"Father" is the only reference to another person in the poem, so it is worthy of some discussion. It really stands out surrounded by so much non-human life—birds, fish, plants, mold. It would appear that Roethke wanted "father" to get our attention. Now that he's got it, let's dig a little deeper into this daddy stuff.
Line 11: Roethke quantifies the depth of Jane's sadness by telling us that it is so deep that, "even a father could not find her." When we think of a father figure in a traditional sense, we think of a provider and protector. But Jane's sadness is so deep and profound that even a father can't help. As we mentioned in the "Detailed Summary," because Roethke refers to a father rather than her father, the word also brings to mind father in the religious sense. This heightens the feeling that, in her sadness, Jane is beyond the reach of even religion and God.
Line 22: Dear old Dad makes another appearance in the poem's last line. In this instance, Roethke wants us to focus on the familial sense of the word. He wants to push us toward considering the speaker's love in comparison to the love of a father for a daughter. What if the poem ended at line 20 with the speaker at the grave speaking the words of his love? What if Dad doesn't show up in the poem's final line? Totally different poem, right? It would be a far more conventional and less challenging elegy since we wouldn't be forced so directly to consider the speaker's non-traditional love for his student.