Question: Most people do not stand up when their parents enter the room. Is this due to the opinion that it is enough to stand for them once in the morning and at night?

Answer: We believe in the great significance of upstanding Jews’ common practices and in looking for halachic justification for them. However, there has to be a good fit between sources/logic and the practices.
The gemara (Kiddushin 31b) gives examples of kibbud (honoring) for parents and of mora (awe). While standing is not on either list, it is evident from gemarot that it is expected (see Beit Yosef, Yoreh Deah 240). This is logical considering the mitzva from the Torah (Yayikra 19:32) to stand before old people and scholars (Kiddushin 32b).
R. Yannai (ibid. 33b) says that a talmid chacham is not permitted to stand for his rebbe more than once in the morning and in the evening to avoid giving to him more honor than to Hashem. The Rif does not cite this ruling, and the Rosh (Kiddushin 1:56) explains (and agrees) that the gemara’s subsequent discussion indicates that his idea is rejected. The Rambam (Talmud Torah 6:8) does accept R. Yannai. The Shulchan Aruch (and, therefore, Sephardim- see Yalkut Yosef, Kibbud Av 4:8) rules like the Rif/Rosh.
The Rama (YD 242:16) accepts R. Yannai, but not according to its simple reading; one is not obligated more than twice a day, but he may do more (see Darchei Moshe YD 242:11; Semag, Aseh 13). Most Acharonim (see Chayei Adam 67:7; Shevet Halevi II:111; Yalkut Yosef ibid.) assume that the exemption applies to parents also. The Aruch Hashulchan (YD 240:24) suggests that the obligation to stand for one’s parent may exceed that toward his rebbe. (I believe, but cannot develop here, that according to the Rambam’s presentation of the case in which it is not permitted to stand more than twice a day, it does not apply to parents. Also note that the Rama rules that when one is among people who did not see him stand previously, he must stand again.)
It is difficult to demonstrate how the Rama’s opinion would justify the common practice of laxity about standing up for parents. After all, do people think about whether they already stood for their parent that day? The Rama can still help, depending on the following chakira about his opinion. Must one stand at the first opportunity of the day, after which there is an exemption, or should there just be a mode of behavior in which he is expected to stand roughly once in the morning and once at night? This might depend on if standing is part of the positive kibbud, making the exact timing less crucial, or the more negative mora, in which case without an exemption, remaining seated is an aveira (Yalkut Yosef ibid. is unsure to which category it applies). This, of course, helps only if the child stands with some regularity, which is not always be the case.
Another minimizing opinion found in the Aruch Hashulchan (ibid.) is that standing only applies 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 practice of laxity is the idea that a parent can be mochel (waive rights to) kibbud (Kiddushin 32a). (Regarding being mochel requirements of mora, see Living the Halachic Process III, G-4.) In our times, parents do not usually expect their children to stand up in their honor and often do not find it to even 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 their mechila, it is a mitzva to stand for parents (Pitchei Teshuva, YD 240:16). Some say that one has to make some gesture of respectful acknowledgement (see Kiddushin 32b). If the reason parents are mochel starts from the children (i.e., the parents are so used to their not standing that they no longer demand or expect), this is not a good thing. Therefore, it is, in most cases, better for children (of all ages) who try to do things properly to stand for their parents more than is presently common.