Researchers have found a correlation between injuries and frequent race efforts. This connection also extends to speedwork, since intervals also require a near-maximal effort. So if you train fast once or twice a week and then race on the weekend, that’s a lot of hard efforts without sufficient rest, particularly if you follow this pattern week after week. Regular speed training is fine for those aiming for podium placements or age-group awards, but it is not recommended for the average runner.
Give yourself plenty of recovery time. A good general rule is to rest one day for each mile raced. So, if you race a 5K, take three days off to rest and let your body recover. If you are trying to quicken your pace for a specific goal, add a weekly or bi-weekly speedwork session to your training plan, but be wise about it.