Some groups are just not as active, and their admins don't check the requests often. I try to stay away from those types as they don't post comments and other things in a timely manner.

Try searching for another OPEN group and you'll see they are more active. Also, join some mobile or SEO or marketing groups.

I got into a couple of closed dental groups. You sometimes need patience and a fully filled out profile.

This is lengthy, and isn't revolutionary or anything, but this is my exact process step by step when I want to enter a new industry of professionals that I haven't targeted before on LinkedIn:

THE METHOD
1. I join 1 active open group and make sure that it's visible in my profile, join 2 if I feel it necessary, like I'm not getting into a closed group.

I also check for quality conversations. I want there to be more conversations about the industry and from the professionals that work in it, than marketers and advertisers spamming "helpful" articles/services.

2. I check the members in the group and see if I already have 1st & 2nd degree contacts in the group that work in that industry (using advanced search to narrow down).

3. Next, see what groups these 1st & 2nd degree contacts are in that are active closed groups, I've found there's more of a chance the admin will be active if the group is active.

I personally only apply to 1 or 2 and wait about a full week for approval unless the admin has an automated message stating the wait could take longer than that. I've waited as long as 2-3 weeks for approval, patience is key for sure sometimes.

I only apply to 1 or 2 because I want to make sure I get approved by at least 1 of them. I don't want to apply to all of the closed groups in the industry that I find at once and get rejected.

4. Once approved, I make sure the closed group is visible on my profile and the open group is not.

I only do this step because in my mind it seems like it brings credibility to your profile that you do actually work in the industry you're trying to get into the closed group for, it's worked for me.

5. Then I apply to get in more closed groups, but I only keep 1-2 of them visible on my profile.

I also only have 7 groups visible on my profile for 2 reasons:

1. Because I believe that's all LinkedIn shows at once now
2. When I'm trying to get accepted into a closed group, I want my profile groups to appear targeted for that industry for the admins that check profiles

6. Lastly, I suggest having something about the industry you do work for on your profile. I can't really measure how well this worked for me because I've changed this a bit on my profile, but I think it helped.

It said something like "who I do work for" in all caps, and a bullet list below that of about 8 industries I'd made contacts in, like lawyers, painters, plumbers, etc.

So in your case I'd have something like
I've changed it now to just 1 line about doing work for businesses/companies that advertise online, still works, but it seems like my accepted response was higher the other way, or maybe I was just targeting more industries so it seemed higher. I mainly have this little blurb in there for the admins that check profiles.

Now, for a little statistics about how this works for me...

MY CASE STUDY
I originally was in 7 groups before I started actively using LinkedIn. 5 open, 2 closed.

Now I'm in 43 total groups, so I joined 36 new groups. 27 are closed groups related to what I do, 23 are industry/niche related to build my business.

Once I started being more active I came up with this method.

I've only not been accepted into 4 closed groups that were industry related to build my business doing this. 3 took longer than 1-2 weeks to accept so I withdrew my request and 1 I was just flat out rejected, no biggie.

So, overall I've been accepted into 85% of the industry/niche related closed groups I've applied to, for me that isn't bad.

Of course, don't know how well this will work for you or anyone else, but this is how I do it and this is what works for me...so no crying to me that this doesn't work. :p

Now getting paying clients that aren't trying to suck my time with free info is a different story.

Try starting your own group geared towards the professionals you are going after. Then, you don't have to worry about joining these other groups as much. Instead, you will have a new revenue/leads stream that you can control 100%!

Sometimes it takes time to accept your request in Groups but try to search for open groups as well.

I think it just takes time.It will be okay within 4 or 5 days.Just be patience.

Sometimes it takes time to accept your request in Groups within one week but try to contact the admin then explain to the admin why interested to join as well.