Wordpres on site or separate domain

I have a client with a main website and a wordpress blog on a separate domain.
The domain name for the wordpress blog has keywords and only performs for that set of keywords.

The main domain performs better for her other keywords.

Would it be best to combine the two into one website with both domains pointing to the same site or keep them separate?

Thanks in advance for any replies.

One of the reasons I was doubtful was that I noticed that when competitors had their blog as a separate domain, then links from there to their main site counted as backlinks.

I don’t think you need to merge your website and blog unless you are getting zero traffic on your blog.

Instead, you can show a path to your audience towards your blog by adding a blog tab or any other button.

Also, you need to optimize your blog a little more to improve your blog’s search engine visibility. Get more backlinks for you blog’s index page and inner pages.

Absolutely correct. I had done the same with our website and blog.

Don’t merge your blog as of now. Waiting for sometime might turn the results the way you want.

Thanks everyone for the helpful advice. Can I ask if the reverse is also true. What I mean is…
If I have a website with a wordpress blog in it, is it worth separating them into 2 domains if the blog doesn’t perform as well as the main site?