I like the second one best, but I'm reading "continvous". This is because you are trying to connect u to o and s from the top of the stem, but this is the conventional point for connecting from v. In some very rounded scripts that connection is the only thing to differentiate u from v.

Also the connection from n to u in the second one does not work as well as that connection in 3 and 4.

I would break the word in two, then stack them and try to find a graphically clever way to make them "continuous".

i like riccard0's suggestion. currently they don't create a continuous feel. on the lines of riccard0's suggestion, wonder if you created space between conti---nuous and tied the 'i' and 'n' in someway. would that create the feeling of continuous i wonder. just a thought.

1. All variants with interconnected letters don't work. I can relate them to some handy crafts business (stitch stuff). And it definitely doesn't work as an ad agency logo. The last one is very nice and clean but the connection between /co/ and /us/ should be removed. letters themselves are very nice, clean and I can relate them to advertising. Majority of agencies use simple and clean sans serifs.

2. I second riccard0's idea. but instead of just connecting them with a sort of line or something you could use ellipsis which we relate (at least I do) to a pause and thinking.

like: conti...nuous

In general I like the idea of having simple and clean type with some kind of continuation. Think of things that pop up when you think of words: "continue", "continuation", etc. Maybe one of the associations will give you an idea of how to make the continuation in your logo.

Sorry but I agree with litera's comment that none of those look like an ad/design agency logo. Perhaps you could explore alternatives that communicate the "continuous" concept in some other way. For example, perhaps letters that are reversed out of background of elements which are joined together. Or a separate logo symbol.

Just a crudely drawn random thought, not sure if it breaks an unwritten rule about keeping logos 1 color...

edit: I would change the typeface to suit and probably remove all other connectors.

No this blue arc doesn't work either because it has the feel of falling. First it goes up then it falls back down... And as you anticipated it would be hard to create a BW version of this logo.