This has not been the case in my experience. I tried several different antennas, but none perfomed very well on lowband if it performed well on highband and/or UHF. I don't know of any base antenna that will perform this feat, unless you are working with well over 40-45 feet in height.
I solved the problem by purchasing a Cushcraft Ringo Ranger AR-6 antenna. I can work six meters incredibly well with this antenna (less than 1.5:1 SWR across the band), but as a bonus when the bands are not open I use the antenna primarily to monitor lowband. It literally sucks in the signals of distant snow plows and IL state police cars at about 25 feet in height, 20-25 miles easy! I use a Diamond Discone antenna to monitor V/UHF and it does very well, but I don't care for discones or Scantennas on lowband or 800 MHz, as that's not their peak area of efficiency as far as I'm concerned.
I also purchased an Antennex 6 dB gain vertical antenna for 800 MHz and it works very well, thus solving the gaps I had with discones.