Are you sure it's the player_weaponstrip? I thought those only worked via direct trigger. Do you also have a game_player_equip in your map? I know if you include a game_player_equip in your map set to "use only," all players will start with no weapons. However, it's not a round to round thing, it only happens if the player dies, so a second unnamed game_player_equip without "use only" ticked set to re-equip a knife and pistol after death can be used. However, this means that both teams will start with the same pistol. A bug may also be encountered whereby weapon slots could get stacked (on my airsoffort maps one can end up with both an MP5 and a shutgun at the same time that they can switch between in the 1st weapon slot like in Half-Life). I don't know if this can also happen in the secondary slot. So basically, the other drawback to re-equipping the pistol is if a player survives a round and had purchased a different pistol it's possible they could now be carrying whatever they bought plus the pistol the map equips them with.
If you aren't also using an equip entity set to "use only" on the map then try naming the player_weaponstrip. I'm not sure if that will work, your problem sounds a lot like the behavior seen when a use only game_player_equip is in the map.
One more note about player_weaponstrip, it strips the bomb, so you can't use it on any bomb defuse maps. You can use a game_player_equip to equip a bomb but it's not what the game recognizes as "The Bomb". It can't be planted and doesn't show up on the radar.