Answer by periblepsis for Bipolar analog latch circuit needed

I won't answer the entire question. But I'll focus on how you might move the input voltage into range of your \$+5\:\text{V}\$ rail and ground.

^{simulate this circuit– Schematic created using CircuitLab}

If \$R_1=R_2=10\text{k}\Omega\$ then \$R_3=560\:\Omega\$. And this means that you can expect something like this:

In other words, the input is clearly shifted into range. This would allow you to set up a reasonable Schmitt trigger with the right bracketing to get what you need. For the range of \$\pm1\:\text{V}\$, find:

So the window is clear from the above. You can set up your arrangement to work with this range, correctly, and get what you need.

Just a thought.

The first image shows a wider range for your input source and what it looks like at the output. The second image shows just your specific \$\pm 1\:\text{V}\$ around zero-ground. And the output there shows your hysteresis box for a Schmitt trigger, if you want to go that route.

All I wanted to do here is to show you how you can passively bring your input into range of your existing positive-only voltage range.

It can be done.