The Doctor doesn't "frequently change fixed points." The only occasions on which we have seen something that was explicitly denoted (either directly or indirectly) as fixed time be altered have been in "The Waters of Mars", "The Wedding of River Song", and "The Time of the Doctor", and in each instance, there is a potential solution for why the Reapers did not appear:
- In "The Waters of Mars", the Doctor alters a fixed point by saving Adelaide from the Bowie Base One explosion, but Adelaide commits suicide and puts time back on the right track mere moments later. There simply wasn't enough time for the Reapers to manifest and caused any significant damage in that instance, and even if there were, Adelaide's suicide would have undone it just like in "Father's Day".
- In "The Wedding of River Song", the disruption of the fixed point at Lake Silencio was destructive to the point of imperiling reality itself. It was said in the episode that a large portion of spacetime had already been engulfed by the distortion, so this was likely too big of a cataclysm for the Reapers to be able to interfere with, and that's assuming that they hadn't also been negatively affected by it.
- In "The Time of the Doctor", the Time Lords directly assist in the alteration of the Doctor's fated demise on the fields of Trenzalore. It was explicitly noted in "Father's Day" that the Time Lords used to keep paradoxes in check and that their absence is what allowed the Reapers to emerge in that episode. In "The Time of the Doctor", however, the Time Lords were not absent.
More importantly than all of that, however, is that the circumstances in "Father's Day" were very specific and unlikely to be repeated. It wasn't just the prevention of Pete Tyler's death that attracted the Reapers. Rose asked the Doctor if he could take her back in time to the moment of her father's death, and she failed to do what she had intended (that is, speak to him as he was dying). She then asked the Doctor if they could try it again, and the Doctor hesitantly obliged. However, upon arriving the "second" time, he said:
Doctor: Right, that's the first you and me. It's a very bad idea, two sets of us being here at the same time.
And then later on in the episode:
Doctor: I know what I'm doing, you don't. Two sets of us being there made that a vulnerable point.
So by saving her father, not only did Rose create a paradox by changing her own personal past and contradicting their whole reason for coming there in the first place (Because if her father never died in that accident, then how could she ask the Doctor to take her to the day her father died in that accident?), but she also did it while there were two sets of the Doctor and herself present at the same time, which made it a "vulnerable point," and by running out in front of her past self, she changed her own personal past within that "vulnerable point" yet again, because when she was first standing on that street corner, she didn't see an older version of herself run out in front of her and save her father.
Such a pile-up of paradoxes and personal past revisions has yet to occur again in quite the same way. Other episodes with similar-but-not-exact circumstances (e.g. "A Christmas Carol", "The Girl Who Waited", "The Day of the Doctor", etc.) all have certain quirks or elements that can rationalize the absence of the Reapers.