First of all, are you doing cloning or expression?
If you are doing protein expression, the host strain must be a DE3 one, which means that has an IPTG inducible T7 RNA polymerase gene copy at the chromosome. You may use BL21(DE3) or HMS174(DE3) strains.
Second, you may check your selective antibiotic (kanamycin, right?), its concentration and if are fresh made plates.
Third, consider that the gene product of your plasmid may be toxic to the bacterial cells.
Maybe I am wrong but it doesn´t look like a matter of mini/midi kits for plasmid preparation.
I've worked with pET28 quite a bit - albeit a few years ago.
If you're producing a stock of plasmid (e.g. as material for a cloning project or to archive a clone for future use), I'd recommend using a MaxiPrep kit from 500mL or 1L of media. The extra yield will make visualizing the pellet easier. You could also try including glycogen or glycoblue to try and better visualize the pellet. Even if you don't see a pellet, I'd recommend you proceed continue the purification - sometimes you can get usable yields from seemingly invisible ammounts of DNA.
In case it helps, I've always found that scaling up the lysis (e.g. using more P1,2 and 3) helps improve yields. Likewise, spinning down the neutralized lysate before using the syringe step simplifies handling.
If you're trying to purify plasmid DNA for *testing* clones (e.g. via RE digestion, PCR, etc.) then I could offer a few tips on getting better yields from Mini and Midi kits.
I raccomend to use the omega biotek mini kit2 starting from 10ml of e.coli culture grown o/n or their midi kit from 100ml of lb culture. In my experience omega biotek kit ( supplied by vwr) supply from 2 to 4 higher dna amount respect the same kit of qiagen, invitrogen, promega or mchanagel.