Yes, both determinate tomatoes and cukes stop producing. Best approach with both when you have a long gardening season, is just to plant new plants of both. But during the high heat of summer neither will do much. Even a place with a "continuous growing season" has hot inactive periods. :)

Indeterminate varieties of tomatoes will also shut down during the high heat of summer but if you keep them cared for and watered they will kick back into production once the weather begins to cool down a bit.

Dave

Determinate tomatoes are programmed to die after a certain number of leaves and flower clusters. Some will produce the entire crop in one or two batches; those are good for canners or mechanized picking.

I've only grown Romas once and planted them out quite late (probably mid-June?); they kept producing till frost, though there were disease issues and later fruit weren't high quality. As you're in SC, you're probably a zone or two warmer than I am, and with a longer growing season, so for you they might not last all year.

A major factor in some regions is the heat. Too hot, and pollen becomes non-viable, so fruit don't set. The relevant numbers are: daytime highs above 90-95 and night-time highs either above 75 or below 55. Some varieties do better in heat than others (cherries, for instance).

Pollination can also fail when humidity is too high.

In my area the big-box stores still have some tomato plants for sale, both determinate and indeterminate varieties.

Here's where you can find out your USDA hardiness zone; enter your zip code on the upper left:
http://planthardiness.ars.usda.gov/PHZMWeb/
Be aware that this is a new map this year, and your area may be a zone warmer than before (though mine isn't).

If you go down to the bottom of the GW page and click on "Member Pages" in the green ribbon, you can add your zone and/or location info to your member info so it will show up automatically.

The zones are most valuable for knowing which plants will survive winter lows, but can also be helpful to people responding to your question. For instance, in SC you might be in the mountains and 7a like me ... or in Charleston (9a) -- big difference in temperatures.

If you have short growing season like here in Texas. Before heat arrives. Best to plant small to mid size tomatoes for fast growth. Early girl. Celebrity. Heat wave. Solar flare

Will they still grow- is it the length of the plants life I need to watch and not the conditions?

Sorry I missed this when I first read your post but missing has addressed it well - conditions is the focus. Given perfect conditions - which sadly no one has - indeterminates would serve us all well. But since we don't have ideal conditions then either type or best yet, a combination of both types, works.

Dave