The first thing that I would check is that your planetary defense units (PDUs) are not garrisoned, because garrisoned units will not be picked up by transports.
If that isn't the problem, I'd next check that the transports have sufficient available capacity to load a PDU. Ground units cannot be split between transports and you need 100 capacity per unit of infantry or special forces*, 200 capacity per armored unit, and 400 capacity per PDU. If you have two PDUs and six infantry units that you want to move and you have three 500-capacity transports with which to move them, you will only be able to do so in a single trip if no more than one of the transports picks up more than one infantry unit despite the three transports collectively having more than enough capacity to transport all eight units in a single trip. This tends to be more of an issue when picking up troops from multiple locations than when loading troops at a single point.
If that isn't the problem and you are using a fleet of ships, then the issue might be the fleet troop loadout, which by default is something like 25% infantry, 25% special forces, 50% armor, and 0% PDU. If you want to customize this, note that the percentages are percentages of troop-carrying capacity and not percentage of units actually carried, so the default ratio in practice works out to something like a 2:1:2:0 ratio of infantry, special forces, armor, and PDUs.*
*The game appears to reserve 200 transport capacity for each unit of special forces, but only 100 transport capacity is listed as being in use for each unit of special forces.