one rewrite url works and another does not.

You have an error in your code, [HTTP::header uri] will look for a header called 'uri', whereas I assume you mean HTTP::uri.

You are also checking for the same header twice so I've put it in one 'if' statement as well as adding a couple of lines of logging that may help troubleshooting. You also may want to consider using string tolower if this is accessed via a browser as URI is case sensitive. Please try the following.

when HTTP_REQUEST { 
    if {[HTTP::header "Host"] equals "intfilings.abc.gov"} {
        if {[HTTP::uri] starts_with "/navigator_icm"} {
            log local0. "replacing host on URI: [HTTP::uri]"
            HTTP::header replace Host "server1.ct.gov" 
        } elseif {[HTTP::uri] starts_with "/EFilingWeb"} {
            log local0. "replacing host on URI: [HTTP::uri]"
            HTTP::header replace Host "server2.ct.gov"
        }
    }
}

You can also perform the same functionality using LTM Traffic Policies, these are recommended for simple iRules such as these.