We believe, as do you apparently, in the great significance of the common practices of upstanding Jews and in looking for halachic justification for them. However, there has to be a good fit between sources/logic and the practices in question.
The gemara[1] gives examples of kibud (honoring) and of mora (awe) for parents. While standing is not on either list, it is evident from gemarot that it is expected.[2] This is logical considering the mitzva from the Torah[3] to stand before the elderly and scholars.[4]
Now let us take a look at the idea of standing once during the day and once at night, which you mention. The gemara[5] cites R. Yannai as saying that a talmid chacham is not permitted to stand up for his rebbe more than once in the morning and once in the evening to avoid giving more honor to him than to HaShem. The Rif does not cite this ruling, and the Rosh[6] explains (and agrees) that the gemara’s subsequent discussion indicates that this idea is rejected. The Rambam,[7] on the other hand, does accept R. Yannai’s opinion not to stand for one’s rebbe more than twice daily.
The Shulchan Aruch does not cite R. Yannai’s halacha, thereby demonstrating that he rules like the Rif/Rosh, and this is the ruling accepted by Sephardim.[8] The Rama,[9] in contrast, accepts R. Yannai’s view, but not according to its simple reading; rather, one is not obligated to stand for his rebbe more than twice a day, but he may stand more often.[10] (The Rama also rules that when one is among people who did not see him stand previously, he must stand again.)
Most Acharonim[11] assume that the exemption of standing only twice daily applies to parents as well, although the Aruch HaShulchan[12] suggests that the obligation to stand for one’s parent may exceed the obligation toward his rebbe. (According to the Rambam’s presentation of the halacha – that it is not permitted to stand for one’s rebbe more than twice a day – it is plausible that it is still permitted to stand for one’s parents more than twice, but we cannot develop this discussion in the current forum.)
It is difficult to argue that the Rama’s opinion would justify the common practice of laxity about standing for parents. After all, do people really consider whether they already stood for their parent that day before deciding to remain seated? Nevertheless, the Rama’s view may still help us understand the common practice. Consider the following chakira[13] regarding the Rama’s ruling, which we will examine through a practical question. According to the Rama, must one stand at the first opportunity of the day, after which there is an exemption, or is it enough that there is a mode of behavior in which one stands roughly once in the morning and once at night? This might depend on if standing is part of the mitzva of mora, which incorporates the acts that must be avoided in order to demonstrate proper awe, or the mitzva of kibud, which refers to positive acts performed to demonstrate honor.[14] If we stand for parents due to the negative element of mora, remaining seated would be forbidden unless one stood already; if it stems from the positive element of kibud, the exact timing of the performance would be less crucial. According to the latter approach, we could justify a certain amount of laxity if the child stands not infrequently, but that is not always the case.
Another factor that minimizes our apparent lacking is the opinion recorded in the Aruch HaShulchan[15] that one must stand only when a parent comes in from outside the house, not when he moves from place to place in the home.
The most plausible explanation for the common laxity in this regard is the idea that a parent can be mochel (waive rights to) kibud.[16] In our times, parents do not usually expect their children to stand up in their honor, and they often do not even find it to be positive. If that is the case in a specific household, then the child is indeed not required to stand.
Let us clarify a few things. Even after a parent’s mechila, it is still a mitzva for a child to stand for his parents, just not an obligatory one.[17] Also, some say that one must make some gesture of respectful acknowledgement.[18] Finally, if the reason that parents are mochel starts from the children (i.e., parents are so used to their not standing that they no longer demand or expect it), this is not a good thing. Therefore, in most cases, it is better for children (of all ages) who try to do things properly to stand for their parents more often than is presently common.