To care does not mean to give everything one can for no matter what.
Providing unconditional care could get tired (easily), and it often brings side effects such as hoping for something in return.
This kind of unconditional care can also bring other causalities if the recipient does not acknowledge and notice the care - for the definition of care is complete only when the recipient receives it knowingly - I believe. Of course, love as in storge is different. It involves the unceasing unconditional care from a parent to a child, and it is complete as long as the recipient receives it. We as kids do not know love of parents, but we realize as we get older, and there is always continuous streams of unconditional care from parents as a kid not acknowledging or as a grown-up acknowledging.
These unconditional cares (other than storge) then often leads to an end in a relationship of two people.
In a relationship, I believe selective and often conditional care is what's required rather than the unconditional one. For that to happen, one has to find weakness that needs to be complemented in the other. Yet it is often very difficult to find all the weaknesses as some are persistent unseen.
Discovering weaknesses does not solve problems either. When the person intending to care discovers one's limits to provide the care one intends and complement the other's weakness, this could to lead to another negative effect on the relationship with despair.
However we should respect each one's uniqueness including ourselves.
We get into relationships not because we find ourselves great match with the other. That certainly is not the primary reason. Despite however the match seems to work, there are always each one's uniqueness hindering the course of a relationship.
The uniquenesses arise from common causes including different family backgrounds, difference in sex, or any events from each one's past. Therefore, observing and finding the other's weaknesses requires a great deal of scrunity and time.
But I believe that when two people give each other time and try hard, this can be done. As each other give time to complement each other, this should help alleviating any unfortunate and unhappy incidents that may occur.
That's why every relation that lasts ignites with endless conversations, and understanding that time is required by each other to understand and provide the necessary care for each other.
Within that time, thinking how to care should be always should be the first step in love, agape.