The difference has to do with their meaning

> *"at"* - refers to a *physical location* <br/>
> *"in"* - while it does refer to
> physical location ***in many cases***, but with your usage, it is
> referring to a *state of being*

If you notice my ***bold and italicized*** words, that is an example of a _state of being_

A clear-cut example is:

> He was *in a **coma***

where ***coma*** is a state of being

A clear-cut example for your usage is:

> They stayed *in contact*

or

> They stayed *in contact with each other*

where *"in contact with each other*" is the *state of being*

I would try to define *state of being* better to you, but in English there is *no way* to define the word *being*, therefore *state of being* can not be defined. The only way to define it is to provide synonyms or explain it to you via examples.

A synonym to *state of being* would be *state of existence* or *state of existing*

**Just Noticed Something:**

In the phrase:

>...their attempts *at contact* with their European counterparts.

technically "contact" is not a real physical location, but rather it refers to a symbolic location on *the timeline*, so the rule here about location still applies