On the interpretation of (51:55)
In this verse Allah says:
And remind, for indeed, the reminder benefits the believers.
After addressing disbelievers reminding them what Allah created and about what happened to earlier nations of disbelievers and pagans. Then Allah reminded Muhammad () that earlier prophets () and messengers () were also called or considered as "A magician or a madman." by their people. then Allah says:
Did they suggest it to them? Rather, they [themselves] are a transgressing people. (51:53)
which is a describing the Meccan's and then Allah concludes His addressing with the words:
So leave them, [O Muhammad], for you are not to be blamed. (51:54)
So the context of this verse is that if Muhammad () stopped advising and reminding the Meccan's of Allah he wouldn't be blamed. While reminding the believers is certainly a benefit for them. Therefore ibn Kathir interpreted this verse as follows:
(And remind, for verily, the reminding profits the believers.) meaning, for only the believing hearts benefit from being reminded. (Source qtafsir)
with no more commentaries. While al-Qurtobi -see here in Arabic- actually added that verse (51:55) is abrogating (51:54) as stated by ad-Dahhak الضحاك while others say it was abrogated by the verse of the sword. He also added some interpretations of the verse for example Mujahid مجاهد said that good advice benefits the believers. Qatadah قتادة said that reminding with the qur'an benefits the believers. And it was said remind them by the punishment and by the days of Allah and Allah emphasized on the believers as they are those who benefits from this.
Allah elsewhere show us then different levels and kinds of the effect of reminding people of Allah in a more general manner:
So remind, if the reminder should benefit; (9)
He who fears [ Allah ] will be reminded. (10)
But the wretched one will avoid it - (11) (87:9-11)
So the verse we discuss is referring to people who believe while those who may believe later are actually -at the time this verse was revealed- one of the categories described in the verses from surat al-'A'la (they might benefit or avoid (reject) to benefit. Among these benefits for the believers we may find (as stated in at-Tahrir wa at-Tanwir التحرير والتنوير see here in Arabic)
- the remembrance and consolidation of what they already know (i.e. of wisdom).
- learning and getting new knowledge of what they have heard or remembrance of knowledge they've forgotten or missed.
- by the day by day strengthening of the believers over the disbelievers and their final victory.
- and the weakening of the positions, objections and arguments of the disbeliever while those of the believers are more an more shown to be true.
Allah also says addressing the believers:
O you who have believed, upon you is [responsibility for] yourselves. Those who have gone astray will not harm you when you have been guided. To Allah is you return all together; then He will inform you of what you used to do. (5:105)
On the interpretation of (69:48)
In this verse Allah says:
And indeed, the Qur'an is a reminder for the righteous. (69:48)
Prior to this verse Allah quotes the most important mission of prophets () and messengers () spreading Allahs message and his revelation addressing the believers by addressing their mind saying that if Muhammad () didn't spread the message or spoke falsely HE would have made an end to his prophets () life. So the speech in all these prior verses is about the revelation: the qur'an.
But it specially addresses those believers that have fear of Allah as HE informed us referring to the qur'an as a source of guidance and a reminder:
This is the Book about which there is no doubt, a guidance for those conscious of Allah - (2:2)
But only as a reminder for those who fear [ Allah ] -
In fact the qur'an is a reminder for fearful believers in all their states as they believe in Allah, in the reanimation, the compensation and the punishment by Allah as he (the qur'an) guided them to faith so whenever they hear or read it they remember about what they know and therefore it is a reminder for them in their whole life be it in their past, present or future.
You may also read in the qur'an:
...Say, "It is, for those who believe, a guidance and cure." And those who do not believe - in their ears is deafness, and it is upon them blindness. Those are being called from a distant place. (41:44)
So on the whole the qur'an and Allah's messengers () and prophets () may remind many people. or might not depending on their faith and their acceptance for Allah's message. But this reminder must not be in vain as it might come later for some of them. However Allah also confirms that the more a person is fearful the more impact the message of the qur'an will have on him/her.