LinkedIn restricts how many times you can post to LinkedIn Profiles and LinkedIn Company Pages via their API (what we use to integrate with them).
The restrictions are as follows:
Profile: 25 updates per 24 hour period.
Company Pages: 20 shares per LinkedIn user - this means that, if you've added two LinkedIn Company Pages to your Sendible account using the same LinkedIn profile, you can post a maximum of 20 messages to both pages in total within a 24 hour period so for example, 10 updates per Company Page.
If you want to send more updates, you'd need to add services for the Company Pages you still need to post to when logged in as another admin of that LinkedIn page.