There is a limit to the number of Adsense units allowed per page per the Adsense ad placement policies:
Currently, AdSense publishers may place up to three AdSense for content units on one web page. This includes a maximum of one 300x600 ad unit per page. You may also place a maximum of three link units and two search boxes on each web page.
If you place more than one ad unit on a page, our system will display unique ads to each ad unit. Because the system automatically displays an optimal number of highly targeted Google ads on each page, in some cases, the maximum number of ads may not always appear. In this case, the ad unit will show as a transparent box, or will contain any alternative ad or colour specified in the ad code.
However, keep in mind that placing the maximum number of allowed ad units on a page may result in it looking cluttered. Read our optimisation guidelines for tips on where to place your ads.