We have an area of paving stones between the driveway and a ground level door.

After they we laid in place (on top of a base level of hot top) I applied mortar between the blocks to stabilize them and to carry of rain water.

Towards the end of winter the mortar started to break up.

Question:
Is there a special, hi tech mortar for such an application? I suppose what I am really looking for is a weather tolerant “grout”. Here on the coast of Maine means a lot of freezing and thawing plus plenty of rain.

I have seen mention of Epoxy Mortar, but would like to steer clear of a two part system.

I saw piece on TV about the use of a concrete coating that include latex and actually stayed flexible.

All ideas will be carefully considered.

on top of a base level of hot top Here on the coast of Maine means a lot of freezing and thawing plus plenty of rain.
....)

Not a problem with mortar in Eastern Main, 70 lighthouses out of masonry/mortar

If this 'hot top" is asphalt and not concrete under the stone.

Explain "blocks' please. Is this a stanard cement block? Or balast from old ships.

The mortar break up is indicative of a moving base not suited for masonry work to be laid on. Explain the base of the stone setting please. It should be concrete if its going to have mortar joints.

Hear how mortar should be thought of. Does it separate the stones/bricks or hold them to together?

Both... It's a dressing to fill in a void and control the distance between the natural material its mating with. Its not designed for shear movement which breaks up the joints. Its intended use structurally is for compaction in strength and a medium that can be adjusted in vertical height which is again compaction. Any horizontal work laterally ( walks) such as exposed mortar joints is simply to keep the water out of those joint so not to freeze and pop the laid material. ( brick/stone/flagstone )

There isn't a mortar that's designed to hold together horizontally for shear movement. I'm a mason and its all in the footer/concrete base under the laid brick walks set in Hi strength mortars as a bed of mortar. The only additive we use in mortar for walks is laticrete and that's not a normal practice. I'm Pa and we get 0 degree temps up to 100 degrees. That's hard on masonry

If you have a good solid base for stone

I agree with 21, what you have is moving around as the ground heaves from frost and thaw. If you are just trying to keep the space between the paving stones filled you could reconsider the 2 part epoxy or even just filling in with limetsone screening.