God's covenant with the Israelites is like a legal agreement: God gets worshipers, his people get protection. (It's a little more personal and spiritual than that, but you get the picture.) Sounds pretty simple, right?
But here's the thing: the writers wouldn't endorse the contract so much if it were a given that everyone was faithful. Would you put up a "no smoking" sign where people never smoke? No. And sure enough, not everyone is faithful.
Much of the Hebrew Bible is spent chronicling the Israelites' failure to live up to the terms of the covenant, either by worshipping other gods or by ignoring God's other specific requests of their people (circumcision, observe the Sabbath, wear "God is #1" foam fingers on Wednesdays, etc.) Check out the Book of Judges for a great example of some covenantal screw-ups. But things don't get too dire until the exile.
Many of the Psalms were written in the post-exilic period, or after Israel was kicked out of its holy land by the Babylonian Empire in 586 BCE (and watched its holy Temple get destroyed). A whole bunch of pious Israelites looked at their disastrous geopolitical situation and got all upset, but then realized that they just couldn't blame it on God: after all, God's supposed to be all-powerful and on their team.
So, they figured that they must have done something wrong. God wouldn't arbitrarily let Israel get squashed...so the exile must've been some sort of divine justice. Israel broke the covenant (must've!), and the exile was their punishment.
In this context, it makes sense that much of Psalms is worried about what happens when God or the people don't do their part. What happens when God stops showing up? What happens when the people stop following God's law? As the post-exilic authors knew way too well, it's not pretty. And if they were a little anxious about covenant, well, who can blame them.