TL;DR: Try to minimize Regular Expression's recursive rules.

Problems

Security Issues
Readability
Premature Optimization

Solutions

Cover the cases with tests to see if they halt
Use algorithms instead of regular expressions
Add timeout handlers

Context

This is known as ReDos attack, a subtype of a Denial of Service attack.

ReDoS attacks can be divided into two types:

A string with an evil pattern is passed to an application. Then this string is used as a regex, which leads to ReDoS.

A string with a vector attack format is passed to an application. Then this string is evaluated by a vulnerable regex, which leads to ReDoS.

Sample Code

Wrong

package main

import (
    "regexp"
    "fmt"
)

func main() {
    var re = regexp.MustCompile(`^(([a-z])+.)+[A-Z]([a-z])+$`)
    var str = `aaaaaaaaaaaaaaaaaaaaaaaa!`

    for i, match := range re.FindAllString(str, -1) {
        fmt.Println(match, "found at index", i)
    }
}

Regex 101

Right

package main

import (
    "fmt"
    "strings"
)

func main() {
    var str = `aaaaaaaaaaaaaaaaaaaaaaaa!`

    words := strings.Fields(str)

    for i, word := range words {
        if len(word) >= 2 && word[0] >= 'a' && word[0] <= 'z' && word[len(word)-1] >= 'A' 
          && word[len(word)-1] <= 'Z' {
            fmt.Println(word, "found at index", i)
        }
    }
}