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After the plant has gone dormant, I would put the container some place cold but protected. In a container, think about duplicating a zone 6 environment. As a side note, sea holly has a very long taproot, which doesn't make it a good candidate for container growing, but that's no reason not to try. Should be an interesting experiment. Here's some more information on these plants: https://www.gardeningknowhow.com/ornamental/flowers/sea-holly/sea-holly-flowers.htm

The plant may not be getting watered deeply enough, especially if it's in a container. If If grown in a pot, make sure to water until it comes out of the bottom. If planted in the ground, water 1-2 times a week for 20-30 minutes or until your watering system has put 2" of water onto the soil.

There are many different varieties of Sea Holly with colors that vary.
Check the tag that came with your plant.

Here is a link that lists some of the common cultivators.

https://www.gardeningknowhow.com/ornamental/flowers/sea-holly/sea-holly-flowers.htm

Yellow leaves normally signal stress of some kind. There are a number of reasons why the leaves may turn yellow. One might be overwatering. Too much water causes yellowing of the leaves and mandevilla do not like overly wet feet. Another possibility could be too little water. If this is the case, the yellow leaves would be curling up as well. This article will help you determine which may be affecting your peach tree: https://www.gardeningknowhow.com/plant-problems/environmental/plant-leaves-turn-yellow.htm

Stress would also prevent the plant from flowering as will a lack of phosphorus. Bone meal added to the soil will help should phosphorus be too low. A soil test will let you know for sure.

There are several cultivators of Eryngium.
Some are hardy down to zone 4 - 5. There are some varieties that are only hardy to zone 8.
If you can identify the variety that your are growing you can determine if it is winter hardy to your growing zone.

https://www.gardeningknowhow.com/ornamental/flowers/sea-holly/sea-holly-flowers.htm

The stems are generally cut back in the fall, but leaving the evergreen leaves on the plant is recommended. These leaves help feed the roots.
Certainly give it some more time to see if the plant can grow back from the roots.
Many times I have though I'd lost a plant only to find tiny signs of life well into the growing season.

https://www.gardeningknowhow.com/ornamental/flowers/sea-holly/sea-holly-flowers.htm