You can keep checking for a lower fare, than originally booked, by accessing your reservation by confirmation number, selecting "change," and looking at the fare showing for your flight. If your flight has gone down in cost, continue the process to change to the lower-cost seat. There will not be a refund of any difference in cost for a paid ticket (not a points booking), but Southwest will hold the savings as a credit under your confirmation number, to be used for futrue travel. Those travel funds must be used only by the ticketed passenger, within one year (travel completed) from date of original purchase.
To use the credit, it's important to save that confirmation number, which gets entered on the payment page of the trip booked within one year.
Southwest will not notify you of any fare reductions. It's the customer's resposibility to keep checking. It can happen - you just need to be vigilant in monitoring the fares.