Grammar

Tirz is right. It depends on the usage. An address of any sort is capped, otherwise not.

The rule you state is just what Wiktionary gives.  Since we don't use our parent's first names, the words we use instead become proper nouns in their places.

But not just direct address.  If I say 'I gave Dad a new saw for his birthday.' it's capitalized because 'Dad' is used as his name.  But if I wrote 'I gave my dad ...' it would not be.

Exactly!

It looks to me like njc was telling us he knows the rules, so would the folks who are messing with him please refer to the website he gave. Too bad the only folks who care enough to read about grammar are the ones who already paid attention in grammar school, as Tirz says. It was worth a shot, though.
When you get real disgusted, please write a sad country western song and post it in the Mama, Trains and Pickup Trucks group. (See how I capitalized?) We haven't had much action there lately.
Keep up the good work.

It's easy enough to remember as child learning the English language that 'your ma' is not capitalized but plain 'Ma' is. The stated rule is a complicated generalization not so easily remembered.

Suppose a father's name is 'Patroclus,' would his son call him 'his Pa' or 'his pa'?   Salvatore "Sal" Mineo's wife might have called him 'her Sal', right? So Pa's son's father is 'his Pa' to him. Therefore, the rule is wrong, and the son's pa, Pa, and his son are right.

Perhaps from the author's omniscient POV, but in those inline reviews for which the reader-reviewer does not read the whole story first to survey the story but digs right in to catch five grammatical mistakes -- I know this never happens, but suppose it might -- he will see "Your Pa has been kidnapped." and nails that bad author. Even from your acceptance of 'Pa' here as a proper noun, how can it be so easily spotted as such from "Your Pa has been kidnapped."? Suppose the author never explains overtly that 'Patroclus'  is a honorific in that long form the character (referent to 'your') never uses, but he always uses 'Pa' , like Sal Mineo's wife never used 'Salvatore', while at the same time 'Pa' is his father thereby being the homophone you suggest. Is such a fantasy of unexplained mystery too cruel to the reader?