QTableView and QSqlQueryModel. Strange problems

[Civil]

I'm writing a small utility. It have QTableView connected with QSqlQueryModel. DB is SQLite3. When somebody inputs text calls findText:

void student::findText(const QString & text)
{
	QString newText=text;
	if (weShouldIgnoreSpaces())
		newText.replace(QString(" "),QString("%"));
	modelQuestion->setQuery("SELECT * FROM Question WHERE QuestionText LIKE '%"+newText+"%'  ORDER BY idQuestion");
	if (modelQuestion->lastError().isValid())
		qDebug() << modelQuestion->lastError();
	modelQuestion->setHeaderData(0, Qt::Horizontal, tr("Question ID"));
	modelQuestion->removeColumns(1,2);
	modelQuestion->setHeaderData(1, Qt::Horizontal, tr("Question Text"));
	modelQuestion->removeColumns(2,2);
<...>
}

void student::findText(const QString & text)
{
	QString newText=text;
	if (weShouldIgnoreSpaces())
		newText.replace(QString(" "),QString("%"));
	modelQuestion->setQuery("SELECT * FROM Question WHERE QuestionText LIKE '%"+newText+"%'  ORDER BY idQuestion");
	if (modelQuestion->lastError().isValid())
		qDebug() << modelQuestion->lastError();
	modelQuestion->setHeaderData(0, Qt::Horizontal, tr("Question ID"));
	modelQuestion->removeColumns(1,2);
	modelQuestion->setHeaderData(1, Qt::Horizontal, tr("Question Text"));
	modelQuestion->removeColumns(2,2);
<...>
}

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(it is part of code).

It seems that it works, but if you write "OSI HUBa" and then delete "a" you'll get what is in attach1 instead of attach2.
If I add

delete modelQuestion;
	modelQuestion = new QSqlQueryModel(0);
	questionOutput->setModel(modelQuestion);

delete modelQuestion;
	modelQuestion = new QSqlQueryModel(0);
	questionOutput->setModel(modelQuestion);

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somewhere before modelQuestion->setQuery it works normaly. But I don't think that it is normal behavior.
I think the problem is in my code. But I don't know exactly where.
Any ideas?