As you've said, being saved is a process more than an event. You can think of repentance as a continual process or something you do over and over again. The definition becomes blurry when you consider something you do over and over again as a process.
Sometimes we look at repentance within the scope of a particular sin, and once we stop doing that thing, it could be said we've repented of that thing. But how long that repentance lasts is up to us. You ask, "How long can I be forgiven of all my sins?" Well, the answer is ultimately the same as any other Christian would give: forever. But that does not come until heaven, and only if we've done our part (2 Nephi 31):
19 And now, my beloved brethren, after ye have gotten into this strait and narrow path, I would ask if all is done? Behold, I say unto you, Nay; for ye have not come thus far save it were by the word of Christ with unshaken faith in him, relying wholly upon the merits of him who is mighty to save.
20 Wherefore, ye must press forward with a steadfastness in Christ, having a perfect brightness of hope, and a love of God and of all men. Wherefore, if ye shall press forward, feasting upon the word of Christ, and endure to the end, behold, thus saith the Father: Ye shall have eternal life.
Also from 2 Nephi 25:
23 For we labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do.
In Moroni chapter 10, Moroni explains that we can "become holy, without spot" if:
33 ... if ye by the grace of God are perfect in Christ, and deny not his power, then are ye sanctified in Christ by the grace of God, through the shedding of the blood of Christ, which is in the covenant of the Father unto the remission of your sins, that ye become holy, without spot.
That is the lifelong quest.
And how do we become "perfect in Christ" (i.e. fully repented)? The previous verse:
32 Yea, come unto Christ, and be perfected in him, and deny yourselves of all ungodliness; and if ye shall deny yourselves of all ungodliness, and love God with all your might, mind and strength, then is his grace sufficient for you, that by his grace ye may be perfect in Christ; and if by the grace of God ye are perfect in Christ, ye can in nowise deny the power of God.
This is what the lives of Latter-day Saints are all about.
It's kind of hard to believe I can really be 100% clean again because there's always more to repent of.
I don't think the record of our lives are tallied and supposed to sum to 0 at the judgment. In other words, I don't think there really is a "100% clean" compared to God.1 Constant repentance is necessary so that we can become who are we are supposed to become.
In summary, being forgiven is something we must always strive for, because while we live in this fallen world, we will be subject to temptation and also the "natural man" (our carnal desires/habits) that King Benjamin talked about. We will be forgiven as often as we repent, and we must repent until we are "fully ripe" (as the Lord told the Brother of Jared). And if we die or rise perfect in Christ as Moroni talked about, our forgiveness will be everlasting.
1. Consider what Einstein postulated with special relativity: even if you were going 99.9% the speed of light, and something moving at 100% the speed of light passed you in the next lane, it would appear to be going the speed of light as if you were not moving at all.