The Texas Department of Public Safety (DPS) states that moving violations appear on a TX driver record for a period of 5 years with the exception of serious offenses.
The TX DPS notes that serious offenses such as DWI and No Liability Insurance convictions remain on a driver's record indefinitely. Their law reference is 37 Texas Administrative Code 15.101.
The amount of time a driving without insurance ticket will remain on your driving record varies by state according to state laws. As noted above in Texas it does not drop off of your driving record put remains on it indefinitely, as does a DWI.
So yes since these types of offenses remain on your record and thus being found an uninsured motorist for a second time allows the DPS to count this as a second offense because the first one did not drop off your record, nor will this one.
If the DPS informed you that an SR-22 is required then it will need to be filed by your insurer. An SR-22 insurance policy is a certificate of insurance that shows the Texas DPS proof of insurance for the future, as required by law. SR-22 insurance is motor vehicle liability insurance which requires the insurance company to certify coverage to DPS, and the insurance company must notify DPS anytime the policy is cancelled, terminated or lapses.
In Texas a SR-22 is required for 2 years from the date of crash, date of conviction or date the judgment was rendered. This is according to the Texas Transportation Code 601.056.
If you want to get a quote for Texas insurance and SR-22, follows this link for free auto insurance quotes.