Well, I play DA, but I think it's similar enough here that I might offer some comments.

First of all, look at the Yor ships/fleets in the viewer and see what their offense, defense, and hitpoints are.  If the Off/Def stats greatly exceed the "nameplate" values the ship(s) has(ve), then the Yor may have some Red bases somewhere.  They may also have put race points into offense/defense, and may have harvested some anomalies to boost their stats a little more.  If the Yor have Red bases, go after them, destroy them, and try to build your own there, with extra modules.

Second, even if the Yor have a little of the "wrong" defense, it will seriously reduce the damage one gun ships can inflict.  Say, for example, your one gunner has a nameplate rating of 10.  Say the enemy has 9 points of the wrong deense.  That still give the Yor ship a defense of 3 against your gun (square root of 9).  The 10 point shot will be modified by a die roll each shot, with the max hit being 10, in the absence of other modifiers (like Red bases). Then it will be compared to the 3 defense.  So, your average shot will be 5, before defenses.  Your ship will take a LOT of combat rounds to kill a Yor at that rate, especially if the Yor has lots of hit points to be whittled down to zero.  Even if your missile is 25 points, that is its max hit, so it's average will be about 12, then there is the 3 points of defense.  If you have taken "luck" and/or Universalist, this will change the math some in your favor, but with a one gun ship it will not help much.

Third, since fleets concentrate on one target at a time, even very serious defense ships cannot survive a fleet engagement if they are targeted.  There is simply too much firepower in the late game.  As a general rule, defenses start out stonger than offensive weapons and lose ground steadily all game after just a few generations of tech.

I am no expert on this game, so maybe others will have better advice.  With that disclaimer, I try to have enough offense on my late game ships to at least exceed the hitpoints of the enemy's largest ships.  A typical design might be 240 offense and 120 defense, though I have gone to 400 - 100 designs sometimes.  It may depend on if I am beams or missiles or guns, as I vary by what I see the enemy building.

Also, I take Luck always, and think long and hard before choosing other than Universalists.  Having Red bases, denying the enemy Red bases, and targeting them first thing are important, very important.

The primary thing screwing you over is the defence stacking. You need some defence yes, but never to the exclusion of almost all your offence and heres why. Defence degrades in battle. It can only abosorb so many of its type of damage before it becomes 0 armor. And the thing is it degrades as you fight, I don't have the math for it handy but the point I am making is that your super defence ships are nothing but a detrement to you. You can go heavy in defence early in the game and it sokay, but by the time you are even halfway down the weapons tech tree you shouldn't be doing that anymore. Also don't neglect your miniturization, its extremely important imo.

Otterbear -

Look at the enemy ships in the viewscreen, maybe write down their stats, then look at your own ships in the viewscreen, then compare the stats.  If you post those numbers here in this thread, you may get some more suggestions, especially if you add the weapons and defense types. 

In case I made a wrong assumption, when I said "nameplate" value for, say, offense, I meant the stats from the design.  For example, if an enemy ship had four 25-point missile mounts, then the "nameplate" rating would be 100 for offense.  However, if the enemy had a 20% racial attack bonus, 39% in bonuses from each of two Red bases (78% total), and had harvested 2% in anomalies, the ship rating would be +100%, or 200 on offense.

So, if you picked out an enemy ship, went to the details page of the viewscreen, and then counted up the doom rays, you could compare that claculated number with the actual viewscreen number.  That delta (above, the ship would have 100 in offense in the details screen but 200 on the viewscreen page) would show you the attack bonus the enemy has.  The higher that apparent bonus is, the more likely the enemy has one or more Red bases somewhere.

On protecting mining starbases, the starbase modules are recognized as inadequate for self-defense.  They mainly serve to require an enemy to send a fleet rather than a singleton.  The way to protect such bases is to place a fleet of your own on the base set for "Guard".  Then, when the enemy gets adjacent and tries to enter the starbase square, you are given the opportunity to defend/attack first with that fleet.  I always fleet protect Red bases and Green bases, and sometimes fleet protect Blue and Yellow ones.  By the late game, the Purple bases have long lost their value.  However, if you still have significant research to be done, they are still worth protecting.

(EDIT - You can sometimes short-cut the above math exercise by using espionage and consulting the enemy's numbers on the race report for that enemy.  That page will provide lots of stats, and that info might be elsewhere, as well.  I often use the math exercise simply because I don't trust the info in those other places as much as the viewscreen.)