The rules for Perception say that you can spend actions (for example, during combat) to keep making Perception checks to notice hidden things.
Can you make active Insight checks in a similar fashion? There are two situations I have in mind:
D&D 4e does not have any rules for "taking 20". However, if you are in a situation where there is no penalty for failure except time spent, you may be able to convince your GM to let you simply spend more time searching, lockpicking, etc.
At 14 rolls, you have greater than 50% chance to roll a 20 (approximately 51.23%, with approximately 48.67% at 13 rolls), so your GM may let you take (time for action) * 14 to "take 20". Alternatively, D&D 3.5 required (time for action) * 20 for "taking 20" (approximately 64.15% chance at a 20), and you might convince your GM to let you port that rule over to 4e.
For reference, 59 rolls would give you a greater than 95% chance at a 20.
Note that you can take a 10 on skill checks in some situations, and in fact that is exactly what Passive Perception and Passive Insight represent.
Additionally, the rules for active Insight checks state "Failure: The creature can’t try again until circumstances change." While your GM make make exceptions, in general (RAW) you should not receive the opportunity for repeated Insight checks for the same thing.
