Would some non-theists just reject relationship with…

Introduction

Clarifying the question
The question most directly relates to the problem of divine hiddenness: if a loving God exists, then wouldn't that God make sure no one is an atheist or agnostic, so that everyone is at least able to be in relationship with God, just by trying?

On the other hand, if some people would just enter into relationship with God but then abandon the relationship later, then plausibly God would lack motive to ensure they enter into relationship. In fact, God might have reason to ensure that they do not enter relationship. The question arises then: would some of those who lack belief in God today, upon coming to to belief, abandon relationship with God later in life? It is worth noting that answering “yes” or “no” is extremely difficult to justify with confidence.¹
1. One reason it is difficult to judge with any confidence whether an individual would abandon relationship later in life is that we are especially bad at affective forcasting:
  - Miles Andrews: “Predicting all of the situations or events that might arise to counter an affective belief state after its initial formation seems to require an omniscience human beings clearly do not possess.” [“Divine Hiddenness and Affective Forcasting” Res Cogitans 5:1 (2014): 108.]

“Yes, after all…

Abandon because: disbelief in God's goodness
A theist might come to doubt or disbelieve in God's goodness. This is relevant because in such a situation, the believer in God could ultimately abandon relationship with God (consciously or unconsciously¹).
1. Here is how the believer could unconsciously exit relationship: in believing that the creator of the universe is not all-good, the “believer” would in fact believing in something other than God: omnibenevolence is traditionally considered an essential property of God's, such that one cannot deny it of an entity while successfully referring to it. One would not be believing in God, but rather some demi-god.
Some would leave due to jealousy of God
A theist might come to grow jealous of God (Perhaps even resenting God).¹ This is relevant because in such a situation, the believer in God would ultimately fail to have a loving relationship with God.
1. - Travis Dumsday: “...one possible reaction is overwhelming jealousy and resentment—jealousy of God and resentment at not being more godlike. The tradition suggests that there is a danger in an immediate awareness of the divine, and that the danger might be mitigated by certain forms of preparation that can only occur in the absence of an explicit experiential awareness of God.” [“Divine Hiddenness and Creaturely Resentment” International Journal for Philosophy of Religion 72 (2012): 43.]
Some would leave due to hating how God allows suffering
A theist might come to forever doubt/resent God for how God handles suffering, perhaps disagreeing with God's reasons or not understanding them.¹ This is relevant because in such a situation, the believer in God would ultimately fail to have a loving relationship with God.
1. See two examples in the footnotes here. It is worth noting that all persons seem to vary to some degree with one another on what issues are wrong and/or to what degree. If objective moral truth exists, then no two of these persons could both be correct. The moral intuitinos of all humans could use at least some calibration. Consequently, if one is going to be on board with God's moral decisions, one will need to trust in God's goodness, as the absolute moral compass, and perhaps even be open to God's moral transformation of the individual, so that their moral intuitions do more closely align with God's.
Some would leave due to love of sin
A theist might come to be closed off to moral transformation, perpetually loving their own sin over loving God. This is relevant because in such a situation, the believer in God could ultimately abandon relationship with God.¹
1. This idea can be further bolstered by adopting anything akin to Eleanore Stump's concept of what relationship with God means. One way of summarizing her view is as follows:
  - Paul Draper (Philosophy professor at Purdue): “(1) God loves me and so desires to be united in love with me. (2) Such union is impossible even for God in my current psychically fragmented condition. To make union possible, I need to be internally integrated around the good and (3) to achieve such integration, I need to undergo a process of justification and sanctification.” [“'Wandering in Darkness: Narrative and the Problem of Suffering' Reviewed by Paul Draper” at Notre Dame Philosophical Reviews (2011) online.]

Would some non-theists just reject relationship with God later in life if they believed in and accepted God (at least in their current state)?

Clarifying the question

Abandon because: disbelief in God's goodness

Some would leave due to jealousy of God

Some would leave due to hating how God allows suffering

Some would leave due to love of sin