Why wouldn't statistics update if all rows in a table were replaced?
Unfortunately after searching SolarWinds' KB for about 10 minutes I cannot find what "Ineffective Statistics" measures. That information would be helpful. However, based on your question I'll infer that it means that the Statistics objects may be out of date or have taken quite a few modifications and Database Performance Analyzer has not detected an update of some sort. Without more information from the product vendor, it's hard to tell. 

Having said that, there are a few things that you should know. 

First, you can verify what's going on with your server right now (e.g. when you get the alert) and compare it against your monitoring tool. Here's a script that I use:

use [mydatabasename];
go
select 
    [schema_name] = sh.name, 
    [table_name] = t.name, 
    [stat_name] = s.name,
    [column_names] = stuff((
                              select ','+index_col(t.name,sc.stats_id,sc.stats_column_id)
                              from sys.stats_columns sc
                              where sc.object_id = s.object_id
                                and sc.stats_id = s.stats_id    
                               order by sc.stats_column_id        
                              for xml path('')), 1, 1, '' 
                            ) ,
    s.stats_id,     
    sp.last_updated, 
    sp.rows, 
    sp.rows_sampled, 
    sp.unfiltered_rows, 
    [sample_rate] = (100.*sp.rows_sampled)/sp.unfiltered_rows,
    modification_counter,
    [default_mod_threshold] = case when sp.unfiltered_rows &lt; 500
                                                   then 500
                                                   else ( .20
                                                          * sp.unfiltered_rows
                                                          + 500 )
                                              end ,
    [2371_mod_threshold] = sqrt(1000 * sp.unfiltered_rows),
    [default_mod_hit] = case when sp.modification_counter &gt; case
                                                              when sp.unfiltered_rows &lt; 500
                                                              then 500
                                                              else ( .20
                                                              * sp.unfiltered_rows
                                                              + 500 )
                                                              end then 1
                                           else 0
                                      end ,
    [2371_mod_hit] = case when sp.modification_counter &gt; sqrt(1000
                                                              * sp.unfiltered_rows)
                                          then 1
                    end

from sys.stats s 
join sys.tables t 
    on s.object_id = t.object_id
join sys.schemas sh
    on t.schema_id = sh.schema_id
cross apply sys.dm_db_stats_properties(s.object_id,s.stats_id) sp
order by t.name, s.name;


Most of it is self-explanatory. However, I added the modification threshold for a statistics object at default and with TF 2371 included. The default threshold is an interesting calculation, while TF 2371 is the square root of 1000 * Table Cardinality. I included a calculation to include whether or not each of these thresholds had been hit yet. So run that inside the alerted database and see if what SolarWinds is seeing comports with what is occurring on the server right now. If it isn't then there's probably a timing issue in there somewhere such that the alert was generated before a stats update but after a massive amount of data change. 

Having said that, it's important to know how AUTO_UPDATE of statistics actually works. There isn't a clock-like sweep that goes through and constantly updates statistics. Instead, the statistics are updated when the statistic object is loaded to compile a query plan. If the statistic is rarely/never used then it won't be updated unless you manually update it or if it happens to get caught up in an index rebuild as a dependent object for the index. However, if you have an index that's never getting used then that's a different situation altogether. 

So in summary:


Verify what the alert is telling you
Know the factors that lead to a stats update