my Piwik counts only a small part of the visitors (1 reply)

Lots of clicks are missing in my Piwik-reports.

We pay for AdWords and in last week we had 1092 paid clicks.

Piwik reports in the same time 1181 visits, but look here:
Details by Referrer Type
Referrer Type | Visits | Actions | Actions per Visit | Avg. Time on Website | Bounce Rate
Direct Entry 408 900 2.21 2 min 8s 68.14%
Websites 400 980 2.45 2 min 0s 61.75%
Campaigns 196 455 2.32 1 min 45s 63.27%
Search Engines 177 453 2.56 1 min 41s 61.02%

Adwords is the main part of the Campaigns, so only about 20% of the AW-clicks are counted in Piwik.
And nearly never I get the keyword reported in Piwik, only sometimes.

For the comparison I also installed OpenWebAnalytics and this counted in same time: 1247 visitors.

In this week we had 21 sales: Piwik reported
Direct Entry 3
Campaign (incl. AW) 4
Google (organic) 4
www.googleadservices.com 8
no hint in log 2

For a larger time frame I had these percentages:
Domains 43 3.47%
Campaign 700 56.50%
Direct Entry 130 10.49%
no hint in log 221 17.84%
Google 145 11.70%
Bing 7 0.56%

Summary: there are a lot of visitors never registered by Piwik.
Any idea what could be the reason for that and how to debug?

Res